To remove a neighbor, just click on your neighbor that you want to delete on the neighbor list below your screen and then there's an option there to remove as neighbor.
Ask him to be your neighbor again
No.
Click on the Neighbors tab, select the person[s] that you want to be your neighbor[s], then click the Add as Neighbor button.
yes
you cant buy a neighbour
dance and click yippee
Yes because you are also listed as his/her neighbor so you will also be deleted in their neighbor's list.
they will be removed but you can add them as a neighbor again
You can get cows on Farmville when your Farmville friends gift them to you or by adopting them when they wander across a neighbors farm and that neighbor posts a notification about it allowing you to adopt the lost cow.
You Can't!
No you didn't lose your current neighbors if you accept other neighbor invitations.