Do Fossil Pokemon need any particular help adjusting to modern life? I plan on raising a Kabutops and I want to make sure s/he will be able to live comfortably and not be freaked out by the dramatic change of scenery by being dead for 300 million years.

Generally, no. So long as you can approximate their diet and living conditions, they should get along well. For example, feed your kabutops meat, offer a pool of warm water for swimming, keep it well exercised and hydrated, and give it a solid surface on which it can sharpen its scythes, and it should thrive in your care.

Of course, there are a few cases in which it might be more of a struggle. For example, archen once ate a very specific fruit that is currently extinct. Some archen may be picky and not easily satisfied by anything but this fruit, which makes the species difficult to raise. However, there is a chance that you may be able to wean it onto a different fruit (persim berries are perhaps the closest fruit in taste, whereas belue is the closest in texture and look) without much of a problem.

Would a fossil fall victim to the culture shock of being brought back to life after 300 million years, however? No. Revived fossils rarely remember the prehistoric era they came from, and those that do are kept strictly for research purposes. Those given to the public, however, are born in this time period and thus are, for all intents and purposes, modern pokémon. They simply act on instinct regarding preferences on occasion.