I wrote like a dozen different grumbly responses about your friend, but in the end decided to just agree with what Infiniti said. If he can trust you to pretend that he's an extra-dimensional elf, he shouldn't have any problems trusting you to pretend that he's an invisible extra-dimensional elf.
Now for a handful of different "at my table"s:
Unless there's a specific meta-game that I have planned for an invisible creature, they stay on the board and I put a white marker under them so that everyone knows that they're invisible and that they've got a -5 to hit them.
If the creature is hidden, and you don't make the perception check, you can't attack it; or more to the point, you can't
hit it. We ignore the whole "you have to guess what square it occupies" and simply pretend that you chose the wrong space to swing your sword.
If the character is trying to snag a hidd-invisible creature in an area of effect, I decide on a case by case basis if there's a chance that they might do it as a smart character, instead of a smart-assed player.
- "I'd assume that he's running for the door." Sure.
- "I'd assume that he's running for A door." Sure, flip a coin.
- "I aim for the two guys he came in here with and hope I catch him in the blast." Why the heck not?
- "I am for this square cause I can see the miniature for the guy right here on the map." Sorry you missed.
Thankfully we all play together nicely and we've not yet had an incident where the players (at least overtly) use their knowledge of where the invisible things are to their own advantage.
In general I leave the enviornmental specifics of what screws over the pee, and en pee cees till after the dice are rolled. In general, dusty hallways and squeaky floor boards are only there after someone flubs a stealth roll or makes a perception check.
To avoid arguments and confusion, spells and effects look like the spells and effects that they are. If you're fey stepping, it looks like you're fey stepping, complete with fey-stepping light and sound and smell effects. When something turns invisible it looks like it turns invisible, and it looks nothing like something that's teleporting. I'm all for reskinning powers, but not in such a way that it makes the powers more powerful. If a player wanted to try to confound and confuse his enemies in a clever way, I'd let them try to bluff (maybe also by burning an action point in the process) them into thinking that they were teleporting instead of turning invisible.
All skill checks are active vs passive so we don't have to keep track of past rolls. If you're hiding you roll against their perception + 10. If they're looking for you, they roll against your stealth + 10.