Can I convert/adapt to PEX from copper tubing?
Yes you can do that (it's the standard way of converting to/from copper), and it shouldn't cause any troubles (read Why would you use copper over CPVC or PEX? and Does Pex tubing have any advantages over copper? for some comparisons).

Of note: you can get the male adapters that fit on the outside of copper pipe, and also that fit on the inside of copper fittings (like a street elbow). Can be handy sometimes if you're working in a tight space, or were going to immediately make a turn anyways (since you're soldering the fitting anyways, it's barely any extra work to do an elbow+adapter, and saves a PEX elbow and couple of crimp rings).