I know if you send a spy to a colony that already has a spy in it, there will be a spy battle.
But what if YOUR spy is landed at your own colony and another player sends their spy to your colony, will there be a spy battle?

Cause I was thinking about stand my spy in my colony to protect it from spies.

spy battles only occur when a spy performs an infiltration so your scenario wont happen

hmmm, I moved my colony, and down sized the settlement left over from the relocate into a outpost and razed that. Its turned into a camp, theres no incoming units, or outgoing, nobody hit it within the 3 ticks it takes to raze and its been a camp for about 20 hours...is the reason its not disapearing because theres a spy there? And if so do I need to send my spy there to take that spy out?

The space im building my hive in is limited to I kinda want that area empty.

Camps do not hurt you in anyway but i guess you could try to kill the spy if you just reallly do not like the camp

Then how about this? Let's say there's a guy X. So X is being teamed up by Y and Z. Now if both Y and Z have their spy's there in X to do damage to X. (Let's say lockdown and injure unit's hp) then what happens to both Y and Z's spy's? Does one operation carry out, only to half the infil points of the other spy, or do they kill one off? Or what happens? Please explain.

when one of the spies performs an action they would fight