How to build more ships?

Yes you can increase all of these to some global max. About 10 or so ships, and 15 or so hangars.

It depends on how you choose your crew composition in the very beginning of a sector map. Put more crew on
engineers and marines to get more max ships, put crew into pilots to get more hangars.

This will mean you will have to take out crew from research but that is the cost of having many ships and hangars