You can find the compound bow rarely in hunting stores, but that’s the second most reliable place to find one. The most reliable place is crafting, as you can find the recipe in a book (can’t remember which one, think it might be welding & metallurgy or the bowyer’s buddy).
It isn’t considered to have higher protection values, just better coverage. There’s an arguement to be made for protection values over coverage, but most of the convos I’ve seen in the forums agree that coverage is usually more important. If you want better protection, just get the survivor suit and reinforce it with kevlar. That gives you 36 cut and 26 bash protection while still maintaining the 100% coverage. If you are really adamant about using the ESAPI vest and are going for a ranger build (as is the most OP in current stable) then you might as well wear both as torso encumbrance has negligible importance for ranged characters.
The grey and sprawling “research facility” is not the same thing as a lab, and is much, much more dangerous. It has extremely high numbers of kevlar zombies and nether creatures, as well as many active portals. You should probably complete a regular lab first before attempting it, just to get a taste as for how to take on larger structures.