Recently I helped a friend switch the gear ratio on his bike from 46:16 to 42:17 and now the chain is far too long, it sits very far back in the track style drop out. I was wondering if this will pose problems in the future or if we should remove links? If so, is there a formula for the amount of links to remove or simply remove a few and see how it sits? Thank you!

When you changed the frt ring, you need to remove 2 full links to compensate. When you changed the rear cog you need to add a half link. The total change needs to be 1.5 links, except that's not an easy option. You'll need to remove either 1 full link or 2 full links (or buy a half link for $5). You'll need to choose based on where the wheel used to sit before the change, if it was close to the front of the dropouts, you'll want to remove one link. If it was close to the rear of the dropouts, you'll want to remove 2 links.

I'd remove one link and put the chain together, install the wheel and see where it sits in the dropouts.

It may work for either 1 link or two links. If that's the case, you'll have the option to sit the wheel in one of two positions (1 link or 2 links). Some people like the rear wheel as close to the front of the dropouts as possible, shorter chainstays have quicker handling. Some like it all the way in the back of the dropouts, should have more stable handling. It's only ~1/2", so the difference is minimal. Also could have fender clearence issues to deal with.

Just take off a link and see how that fits, nothing difficult about that.