Welcome to Eorzea!

Unfortunately I can't really help you on your first question, as I play on the PC version and use a keyboard for targeting, but I do know there is a target filtering system in the system settings which can be adjusted so that the cursor will automatically select only certain targets, or disabled completely.).

As for your second question, a 'Free Company' is much like a player Guild from other MMOs - they're a formal organization of players who work together like an actual group - they feature things as having their own housing, access to a communal 'company chest' where items and gil can be stored for use by all members, and having bonus status effects that can help members (like exp bonuses, reduced teleporation rates etc). As well, FCs also can have their own crest which the owner can design and which members can have appear on their armour, which really helps a player feel like they belong to the group.

You can only be in one FC at a time though, so if you want to join another one, you'll have to first leave your original one. FC owners like to advertise in the server forums, so take a look at the section for your server (Balmung), and I'm sure you'll find one recruiting (especially as Balmung has a very large roleplaying community so you're highly likely to find one that is more than welcoming of a new adventurer!).