I'm going to start with the easy one: gunpowder. I do that so that I can show you some options to see where you might go if you adjust your world to be easier to realize. You will need to adapt their culture along the way. How much you adapt it is dependent on how much you decide you really need to keep for your world.
Sometimes science and engineering seem very directed, and some articles like "The KMOS Redshift One Spectroscopic Survey (KROSS): Dynamical properties, gas and dark matter fractions of typical z~1 star-forming galaxies" (arXiv:1601.03400) may defend this belief, the majority of such discoveries have consequences far beyond their initial expectations. To choose an example by smooshing together two posts I've recently read: Alan Turing never expected to have an attempt at redesigning currency, like Bitcoin has. It's going to take some work to make a world which is more advanced than us in some medicinal fields, and yet 1500 years behind on basic chemistry. It was quite a feat for the Chinese to invent the stuff back then. Nowadays, if you really understood what your highschool chemistry teacher was telling you, he or she told you all you needed to know to figure out how to make gunpowder. The chemical equation for gunpowder may be a bit messy:
$6 KNO_3 + C_7H_4O + 2 S → K_2CO_3 + K_2SO_4 + K_2S + 4 CO_2 + 2 CO + 2 H_2O + 3 N_2$
but it turns out you don't even need to get it right to understand combustion. One commonly offered simplified version is:
$2 KNO_3 + S + 3 C → K_2S + N_2 + 3 CO_2$
Now this is simple enough that you might even see it on a high school chemistry test. Advanced medical science without a single member of the society that knows basic high school chemistry? Possible, but it shows just how hard we are going to have to dig to accomplish you goals. And it gets harder. Addressing Sean Boddy's comment, gunpowder is only one of many compounds that go boom. In fact, it's not even all that good of one by comparison. As a society evolves it is going to come across hundred of explosive compounds, any one of which could replace blackpowder's role. In fact, it may be worth noting that nobody uses black powder anymore except fireworks manufacturers and war reenactors. It has been completely and utterly replaced by more powerful compounds. Getting rid of all of them may be as hard as getting rid of the air we breath (literally. Nitrogen based compounds are a big deal in the explosives world, but plants are rather dependent on nitrogen). Many of these compounds even work underwater.
The solution is to set up a world where the society does not reward the discovery of black powder. Maybe they have all the pieces put together. Maybe they even know how to use it, but maybe it just isn't a social option.
One option might be a world with a world religion that prefers slow and steady movements. Members of the society are expected to be in control of their actions at all times, and once you pull the trigger on a gun or explosive device, you are no longer in control. Maybe quick flashes like that are reserved for Gaia, and the ultra-pure priesthood. Sure, you might know how to make gunpowder, but it would literally be heresy to make it and use it.
Maybe the society was given their advanced medical tech, with an expectation that any failure to control the proliferation of explosives would result in being cut off from that tech.
Maybe their society is more centered around life energies, rather than physics. Maybe they literally just don't see the value in the ability to disrupt another life as much as an explosive can do. Failure to see value in something is a powerful way to prevent it from being developed.
Now all of this has been focused on gunpowder. What about travel? Travel actually cuts down your number of options noticeably. Basically, you don't want these guys to travel. Modern medicine includes things like control of electricity, magnetism, computers... freezing embryos is actually a lot more advanced than just sticking them in the freezer under your fridge.
With this, I think you collapse your options. It's still valid to have all of this medical technology handed to them by a benevolent alien with a request never to make blackpowder or any modern vehicular travel. However, its almost impossible to fail to develop some kind of useful mechanized travel with the basic tech needed to do medicinal techniques like you describe.
My vote would be for a Gaia world, where it is recognized that the planet is alive. A society built around this belief would develop amazing control over nature and natural processes, but may never learn chemistry. For example, one of the big advances in embryo crypreservation was Slow Programmable Freezing which rely on complicated equipment to carefully control temperatures. However, this sort of slow smooth control is something life excels at. It would be easy for them to adapt a life-energy based approach without actually needing to understand the chemistry.
This would also explain travel. Someone who depends upon life as much as they would wouldn't use a coarse automobile or similar mechanical device to travel. They'd use organic life to make it happen.
In all, you are going to need to find a way to make them not only "not want use blackpowder and mechanized travel," but actually "want to not use blackpowder or mechanized travel." Something in their culture is going to have to actively oppose it the entire way. And whatever that is, it is going to have to reinforce itself for thousands of years to make sure nobody ever gets a different opinion.