TL;DR: Yes, it's fine to cut meats before cooking.
Another option to pan cooking
You might consider using a sous vide cooker (or water bath with a good thermometer) to thoroughly cook the meat before searing. This works by keeping the meat just below the temperature that makes the proteins bind up and squeeze out liquids (see below). The result is meat that is always perfectly cooked to the done-ness you want (pro-tip - use Ziploc or silicone bags, not vacuum sealing, to make it simpler). Then, because it's already done cooking you take the meat out of the bag, put a little butter in a very hot skillet, and sear the meat on all sides just long enough to brown. Result - perfectly done inside, tasty caramelized skillet cooked outside, without having to worry about if some part got under-cooked. I've been doing this for years, and have never even had a mediocre steak since I started it. That isn't bragging. It's just that easy.
Food too large for the pan
You are correct that cooking just about anything with edges lifted in the air will result in those parts under-cooking compared to the rest of the food. As for cutting steak, doing so before cooking will not result in lost liquids, etc.
How to cut
When sizing meat for a certain pan size, be sure to cut across the grain. Meat fibers run in strands that can be tough and stringy if cut so they stay long. Cutting across these fibers cuts them short, so they are easier to chew, and results in meat that can seem more tender.
Regarding lost liquid in meat
For just about all meat cuts, as the meat heats, at certain temperature points the meat proteins tighten up. Think of a Slinky toy stretched out, and then pushing it together. As they tighten, liquids are forced out of the muscles. That is how we get dry meat from cooking too hot.