Depends on your kingdom management. Some might limit only the selected few alliances can enter KvK map.

Yes and you must also have lv16 City Hall and above.

nope, you can enter if u want to, no problem at all

just they may burn your city and zero u if you are not allowed to enter 

of course, you can always revenge because your hospital will always protect certain number of your troops and they wont die, use these troops to kill all their farmers for revenge 

when they are busy killing enemy at the front, you burn their farmers at the back