Just learning the game, and writing down things as I come across them -

1. When after revealing a red maneuver is the stress token actually applied? i.e can I perform a green maneuver while stressed, remove the stress token then perform an action in the same activation phase?

2. If I reveal a green maneuver while stressed, but collide into another ship, does the stress token still get removed?

Just learning the game, and writing down things as I come across them -

1. When after revealing a red maneuver is the stress token actually applied? i.e can I perform a green maneuver while stressed, remove the stress token then perform an action in the same activation phase?

2. If I reveal a green maneuver while stressed, but collide into another ship, does the stress token still get removed?

1. You move your ship, then check for pilot stress. So if it was red, you immediately apply the stress token then. Next comes the Perform Action step, but you can't perform an action, any action when you've got a stress token. If you reveal a green when you're stressed, you move your ship, check stress, remove the stress token, and you can perform an action (if you didn't overlap something that is).
2. When you reveal a green maneuver, you move your ship, and if you overlap another ship, you follow the rules for overlapping, but the maneuver still counts as a green maneuever (even if you couldn't fully complete it), so when you check for pilot stress, you get to remove the stress token, next would come the Perform Action step, but because you overlapped another ship, you skip that.

A stress token will stop you from performing any actions and you aren't allowed to choose a red maneuver when you've got a stress token. Other than that, it doesn't stop you from performing a green or white maneuver. If you do reveal a red while you're stressed, you must hand your dial to the opponent and he chooses any non-red maneuver he likes for you. But beware, they can fly you into another ship, or onto an asteroid or even off the board, so it pays to be extra careful choosing maneuvers when you've got a stressed ship.

If your opponent chooses a green maneuver, does that remove the stress token?

Yes, you execute the choosen maneuver just the same as if you had picked it your self.

I think you will find it rare your opponent would choose green for you in that situation though

I play against an 8 year old, nothing is beyond the realm of probability.

When you reveal a green maneuver, you move your ship, and if you overlap another ship, you follow the rules for overlapping, but the maneuver still counts as a green maneuever (even if you couldn't fully complete it), so when you check for pilot stress, you get to remove the stress token, next would come the Perform Action step, but because you overlapped another ship, you skip that.

Note that this also applies if you perform a red maneuver and overlap. And if it's a K-turn, you do not complete the turn; you move until you overlap, resolve that, then gain a stress for a red maneuver.

Under the Activation Phase in the recent Rules Reference Guide

1. Reveal Dial

2. Execute Maneuver

• Move Ship
• Check Pilot Stress (assign 1 Stress token if Red, remove 1 Stress token if Green)
• Clean Up

3. Perform Action

You can check the Rules Reference Guide online as a PDF, along with the most recent FAQ on this page: https://www.fantasyflightgames.com/en/products/x-wing/