I'm going to consider hydrogen/helium rich warm gas giants like Jupiter and Saturn, here. Things are different for cooler ice giant worlds, so I'll leave those for another day. I'll use "gas" instead of "air" to refer to the planetary atmospheres, and hence "gascraft" instead of "aircraft", etc.
The biggest problem you'll have with hydrogen-rich gas giants is atmospheric density. Even when the atmospheric pressure is friendly Earth-sea-level like, densities will be a fraction of the density of our atmopshere (which is why hydrogen balloons float up on Earth, obviously). Lift is proportional to density, which means that wings for use in a gas giant atmosphere are going to have to be pretty big... as a ballpark figure, perhaps 10 times as large, to generate the same lifting force as a wing on Earth.
This will only be compounded if you want to live on a huge world like Jupiter, where gravity is already more than twice as strong at the altitude where you'd find Earth-like pressure, so you'll be wanting wings that are more than twenty times bigger!
On the bright side though, drag is proportional to density. Drag is also proportional to velocity squared, so you could travel at 3.5-4x the speed you might in Earth's atmosphere for the same amount of effort. Lift is also proportional to velocity squared, which means that for high speed aircraft you can make up for the lower lift provided by the thin atmosphere. The speed of sound in hydrogen is also about 4x higher, so you can travel much faster and still remain subsonic.
So, take-home message: no low-speed gascraft that use wings for lift. High speed gascraft might look more like lower-speed aircraft on Earth. Because winged gascraft will likely be travelling really fast, you won't want them going too close to habitats and other facilities for safety reasons. Their bases (gasports? gasbases?) will be therefore well separated.
If you're not going anywhere in too much of a hurry, use a lighter-than-atmosphere craft, using the same floatation devices your habitats use. Remember again that the low-density hydrogen atmosphere means low drag, so your zeppelins can travel much faster than they could on Earth. Escape craft, escape pods and parachute-equivalents will also need to be balloons of some kind to either stop descent or delay it for long enough to affect a rescue!
I'm not going to attempt to work out the issues helicopters might face. Maybe another time. If your fusion reactors have a good enough power-to-weigh ratio, it may be possible to make vehicles or platforms that can hover and station-keep for extended periods of time using orientable or downward facing jets or fans. This might be a way to allow your super-high-speed winged aircraft to approach habitation safely at low speeds without needing to be bouyant.
You've suggested metallic hydrogen as a useful monopropellant, implying that in your universe it is definitely metastable at sensible temperatures and pressures. However. There are a few issues with the substance listed on Project Rho. One of them is that the temperature of a rocket engine using the stuff is very high (like, engine-vapourisingly high), and even if you use hydrogen as a coolant you'll still drop your Isp to a mere thousand seconds or so. Not bad, compared to mere chemical rockets, but not really enough to easily get you into space in such a deep gravity well.
Secondly, that whole metastability thing. It packs about 50 times more energy than TNT, per unit mass, and you probably don't need to apply much oomph to it to make it cook off. Everything fuelled with metallic hydrogen should be considered a bomb (or missile) until proven otherwise, and should be used and parked at a very safe remove from most habitation and industrial facilities. It might not even be safe to use it too close to nuclear reactors, if there's a chance that a stray fast neutron or suitably energetic gamma-ray might push a little blob of the stuff over the energy barrier and into explosive decomposition.
Another take-home note: metallic hydrogen is hugely dangerous, and no-one will want it used anywhere near anything.
With regards to space-capability, that's a tricky one, something that's heavily dependent on how massy your gas giant is. But, TL;DR: metallic hydrogen is not going to get you into orbit, even before you dilute it to stop your rockets melting.
The first thing to remember is that gas giants are big, and to get to the equivalent of Low Earth Orbit where you'll be at least temporarily stable, you'll have to fly up pretty high and that means you need lots of energy. To lift an object from the Earth's surface to a 250km altitude, you need to provide at least 2.4MJ/kg (note: this excludes the energy required to reach orbital velocity!). You need 10 times as much to reach 1000km over the 1-bar level on Jupiter, and you might not even be far enough above the atmosphere to be able to maintain your altitude as long as you would at 250km on Earth.
Orbital velocity at 1000km above Jupiter is ~41km/s. At 1000km above Saturn is ~25km/s. That's a huge around of delta-V you'll need, on top of the steep gravity well you're trying to climb out of, and in the case of Jupiter, you'll be needing rockets that can deliver more than twice the thrust of their Earth-equivalents at the same time as lifting all that stuff out. That's a pretty tall order, and might require some seriously powerful nuclear rockets to get you out. An Orion drive might be worth considering here.
Of course, you don't need to orbit; as you pointed out, getting above the atmosphere seems like a good way to cover long distances in a sensible time, if that seemed important. Boost-glide vehicles are probably what you want there... long, low suboribtal trajectories that skip off the upper atmosphere. The aerodynamics and design of such vehicles will be quite different from either the large-winged fast gascraft or bouyant slow gascraft mentioned above, and trying to combine multiple modes of operation is probably just asking for inefficiencies. Don't compromise; specialise. The environment is already punishing enough without silly designs and unnecessary extra engines and control systems to make flight more inconvenient!
For chemical fuels (and indeed, for some or more of the elements that you'll need to keep your habitats running) you will have to either a) ship it in from elsewhere (such as the Jovian moons) or b) harvest it from deeper in the gas giant's atmosphere. Jupiter, at least, has ammonia and water cloud decks, which should offer excellent sources of nitrogen and oxygen. You need to drop perhaps 100km below the 1-bar altitude, and the pressure will rise by a factor of ten and the temperature will at least double (which is inconvenient for bouyant vehicles) but it is doable. Other gas giants may also have handy things like methane clouds for carbon sources.
(Atmosphere of Jupiter)
I'd be inclined to use fusion for as much as possible though, as chemical harvesting may well be less convenient that deuterium and helium-3 refining at higher altitudes. The energy densities of chemical fuel are much lower, and there are probably more useful things you could do with the materials than set them on fire.
Nuclear ramjets will be able to go pretty fast in a hydrogen atmosphere, and so might be useful for medium-haul travel, if you actually have need of such a thing. Nuclear jet engines might simply be a better alternative, because gas giants are big and interesting stuff will either be close (because that's where you build it) or far away (for whatever reason) and so there may be little need for a middle ground between boost-glide and scramjets and turbines. Up to you, though.
And as some responses to KeithS's excellent answer:
- Inert gas is of course readily available in the form of helium. There may be some mileage in your habitats and vehicles having an outer pressure hull of helium at slightly above both internal and external pressure. This makes it easier to keep your hard-to-replace atmospheric gasses like oxygen and nitrogen (and even carbon dioxide!) inside, because they can't simply leak into a higher-pressure buffer. In an emergency, helium can be dumped if it starts leaking into habitable areas, equalising pressures whilst leaks and scrubbers are fixed. It is easy enough to replace.
- Building and maintaining a network of JPS satellites is an excellent idea, but for safety reasons you might consider having atmospheric positioning systems too, because if TSHTF it could be very, very difficult to fly up into orbit to replace or repair infrastructure. It might even be easier to do some of this stuff on Jupiter because lines of sight at so very long... there's a reduced need for clever over-the-horizon low-frequency things like LORAN when it may well be possible to use VHF-based marker beacons, driven by fusion reactors for high power, with vast ranges. After all, gas giants are likely to be sparsely populated, and whilst mobile beacons don't help with global navigation, most navigation is likely to be local anyway and a suborbital hop can point in the approximate direction of another habitat's marker beacon cloud and targeting can be refined as a fix is acquired.