I missed the midweek and I just saw my punter is out and I need to sign a new one. Is there any way I can avoid the AI messing up my depth chart?

Hm, there's not a way to sign a punter and make him active and in your depth chart. A signed player will be added to your roster as an inactive player, your depth chart will only get shuffled if you have too many players on your roster or too many active. As long as you cut or IR a player so you're below 53, and have at least 45 players active, the AI will leave you alone if you sign someone; he just won't play in the upcoming game because he'll be inactive.

I'll have to think about the best way to handle that situation - because I'm sure you're not the first nor will you be the last to miss a midweek - but I'm not sure what that would be (maybe adding pending contracts to your depth chart screen or something like that)

So what would happen if I keep 45 active and leave no punter in the depth chart? Would the AI activate the newly signed player and put him in there (even if it shuffles the rest of the depth chart)? Or is there no way I can get the new punter to play?

The AI will not activate the new punter - if you have no one in your depth chart, he'll choose the best player available to punt. If you only have 45 players active nothing will happen to your DC. If you have 44 or fewer active, the AI will rebuild your depth chart, which will activate the new punter but will also restructure the other positions.

Ok, thank you, I'll have to think about my strategy then

Could we have a active/inactive selection when signing?

That's a good idea and shouldn't be too hard to implement. I'll put that on the short list.

So he wouldn't be in the depth chart but the Ai will choose him if the depth chart position is empty.
This would not help a position where the new guy will be your second best player if you have more than one player in the position (eg WR or CB), but I guess you could've clear the whole position leaving it empty and then the Ai will pick all the WRs in order each play. Is there a downside to this?

Well, in general it is usually not a good idea to put your trust in the AI, he'll likely do something weird. In theory, though, your idea would work, you just run into the unpredictability factor.