Mismatched front and rear derailleurs ok for 3x7 setup? I'm thinking of fitting a Shimano Alivio rear derailleur and Shimano Tourney front derailleur to my 3*7 speed. Are they compatible with each other? Will I have to put same levels of derailleurs?
As long as the derailleurs match their shifters and their sprockets, you should be fine.

The front and rear derailleur are not attached to each other in any way. So it's no problem to mount different groups on one bike. 

Its probably a good idea to at least stick to one manufacturer.