Well, Draft85 predicted the inevitable appearance of the atmospheric escape diagram, and as no-one else has been forthcoming I guess it falls to me.
The missing scale on the right for the gas lines should be "ten times RMS thermal velocity at surface temperature". This isn't quite the right model of atmospheric escape but it'll do as a starting point.
You can see that the lower limit of water vapour retention in the atmosphere at Earthlike temperatures coincides with a surface escape velocity of ~7kms. If you actually work out what ten times the RMS thermal velocity of water is at 273K, you'll find that it is more like 6.15km/s, but a) I'll follow the rules of the chart because it looks pretty and b) you don't wanna be right on the edge because then climate fluctuations can cause your atmosphere to fall off. If you do choose this limit, you can knock about 10% of the surface gravity figures below, but I'll stick with 7km/s for now.
Escape velocity is $v_e = \sqrt{\frac{2GM}{r}}$ where $G$ is the gravitational constant, $M$ is the planet's mass and $r$ is its radius. That's slightly too many unknowns, so lets narrow it down a little.
The mass of a planet is proportional to its volume and density, and so for a spherical world $M = \frac{4\pi\rho_pr^3}{3}$ where $\rho_p$ is the density of the planet. Rearranging the escape velocity formula from the wikipedia link above and substituting the equation for mass given density, we get $\sqrt{\frac{3v_e^2}{8\pi G\rho_p}} = r$.
The density of Earth is ~5500km/m3, and lets use that for your world, too. This means that the smallest world with Earthlike density that might hang on to an Earthlike atmosphere has a radius of ~4000km, a mass of ~1.5x1024kg. This is smaller than Earth and Venus, but bigger than Mars. Surface gravity is ~.63 of Earth.
If you used the density of a much less metallic world, like Titan (~1900 kg/m3, mostly rock and ice with little iron) you end up with a larger world... a radius of ~6800 km makes it bigger than Earth! The low density means that surface gravity is lower... a Mars-like .37 gravities. That helps make your people fly more easily and your animals grow much larger, but conversely the absense of a heavy metallic core means that your world will have no magnetosphere and so the atmosphere will probably be blown away by the solar wind (as happened to Mars) or would need to be so dense and thick that the surface would be uninhabitable (as happened to Venus). That's not to say that it is impossible, but it will be hard. You'll also have to deal with your planet being a water world, not at all jungle like!
A compromise Mars-like density of ~4000 kg/m3 gives you a radius of ~4700 km and a surface gravity of ~.52 gees. The surface would definitely be solid, but the lack of a strong magnetosphere may limit the longevity of the atmosphere.
So:
Ish. I'll assume the conservative .63 gravities from here on.
- Giant creatures (not quite Godzilla sized, but bigger than Dinosaurs).
I don't see why not... with two thirds of the gravity of Earth, structural engineering has become more forgiving. You still probably won't get anything Godzilla sized without magic, but you could certainly have things that would tower over the tallest sauropods.
Remember though that the lower gravity means that bones can be thinner and lighter and less muscle mass is needed to hold up bodyweight, so you will find that many of the animals here may seem quite spindly compared to those on Earth... tall, but thin.
- Human explorers should be able to jump incredibly high there, maybe even fly/float (with the aid of some sort of device?)
Maybe. Humans will certainly be able to jump higher, but they'll have to work to keep their muscle mass in low G.
Humans can fly under their own muscle power on Earth with the aid of suitable mechanisms... under a two-thirds gravity that would become something that merely very fit people would be able to do instead of the worlds most elite endurance athletes.
A very dense atmosphere will help here, but having a dense atmosphere without risking runaway greenhouse effects is hard. Keeping a dense atmosphere on a small, warm world is unlikely. Titan's atmosphere is very thick, and it has quite low gravity, but the surface temperature is so low there's little risk of everything boiling away into space. You could probably handwave higher surface pressure if you wanted, and tweaked the atmospheric composition appropriately.
- Humans don’t have to be able to breathe there (I’ll give them air tanks), but the creatures do.
- The atmosphere can be made of anything that will make this more possible.
You could have an Earthlike oxygen-nitrogen mix, and then sprinkle in whatever you like for flavour. You could have 10% CO2, for example, which the local wildlife coudld have adapted to but would be unpleasant and swiftly fatal for unprotected animals from Earth, including humans. A fairly simple respirator with a CO2 scrubber would allow the native atmosphere to be breathed just fine without the need for gas bottle, but the scrubber material will need to be replaced after a few hours of use.
High CO2 implies additional greenhouse warming, which would require your world to be a little further away from its Sun than Earth is.
- (Optionally) the planet should be jungle like, or ocean like, if either of those allow for it to be more possible.
Whole planets don't get to be just one biome. There will be hot bits, dry bits, cold bits, wet bits. Seas and mountains. There can be enough jungle for your needs, it just won't cover the whole planet.