Q: Do mines degrade through attrition?
A: Yes. One or two screen pixels per explosion.
Q: Is there any way to breach minefields?
A: The best way to deal with minefields in TacOps is to go around them if possible. The current scenarios do not last long enough to justify having engineers in the game to do it right. If you feel you must go through, the best current way in TacOps to breach is to send an infantry unit through. Infantry draws a lot less booms per meter than vehicles. Units mark a path as they progress through the minefield with or without booms. I have no plans of adding foot engineers, but I will likely eventually add mine plows and vehicles that throw line charges. Arty does not degrade minefields in TacOps.
Q: Why can't I place artillery-delivered minefields and fire missions at the edge of the map.
A: I put a check in the program that prevents laying of mines, and sometimes fire missions, within 500 meters of the west or east map edges. This is partly a needed program constraint. Mostly it is an arbitrary response to one of my early game opponents placing artillery delivered mines right up against the edge of the map in order to nail my units as soon as they came on the map - boring. It seems a bit less than sporting to not let the enemy at least get in the game.
Potential game problems with miefields
Minefields do use a lot of memory (they are manipulated as regions) and they can fragment the heap over the course of a very long game.