When voluntarily inflicting 1 strain on yourself to get a second maneuver, does that second maneuver replace your action in the round or is it in addition to?

You can either 1) suffer 2 strain to perform a second maneuver or 2) trade in your action for a second maneuver. Either option is distinct from, and exclusive of, the other.

However, keep the in mind if you take the 2 strain to take a second maneuver and then accomplish something that would grant you a free maneuver on your turn you would lose it. You fan only take 2 maneuvers on your turn no matter the source.

You would still be able to take a free maneuver if something grant it you on someone else's turn.

To answer the OP's question: Yes, you can still take an Action after buying a second maneuver with 2 strain. The only thing you can't do, as awayputurwpn said, is also exchange the Action for a (third) maneuver. But you can make combat checks, skill checks and so on even if you have already taken two maneuvers.

However, keep the in mind if you take the 2 strain to take a second maneuver and then accomplish something that would grant you a free maneuver on your turn you would lose it.

You could, though, spend the two advantage on recovering the 2 strain that you spent back.

It's nice that you don't have to worry about that from an opportunity cost perspective.

Great, thanks everyone! I'm the doctor of my crew, so I wanted to see if I could pull a stim from my backpack, apply it, then follow it up with a medicine check. Good to know that I can! The 2 strain looks like a good balancing mechanic so that this particular sequence is generally saved for emergencies.

You fan only take 2 maneuvers on your turn no matter the source.

I know this is quoted throughout the rules however it is not entirely true the Mercenary Soldier talent Field Commander does state that the extra maneuver produced does not count against the number of maneuvers that they may perform in a turn, allowing for 3 maneuvers (with improved field commander and a triumph roll you can allow people to break the one action per round limit instead )