Okay I just got a squad and I need some tips on battlefielding tactics.  What is the recommended pattern for attacks? how do you effectively battle? 

Rolls are random, so just hope for the best combination. It's pretty obvious, but try not to get any pets with negative manuvers. Compensation won't do any good either if no squad member has the bad stuff. Try not to use more than two Leaderships as well. Cockatrices, Rocs, and Symurghs (or actually any other species with high-scoring attacks) with Confusion, Massive Wings, and Song of Peace are incredibly helpful. If you have any dragons with both the Fire Strike and Counterstrike gene combos, use as many as you can. Counterstrike is really quite effective. As for moving around and attacking, I usually look at all the pets in the squad before attacking becuase losing all of your energy with one objective and having it go to waste it not fun. Also, try to stay in a fairly open area. If someone defeats you while you aren't online and there are no open zones around you, leaving the island is what you get.

Does levels, gp and increased stats effect the performance of battling?

Levels don't really matter. GP (depending on how much the pet has) provides extra manuvers and above 100 of certain stats allow you to use two of a specific manuver such as if your pets has Silent Pace and Agility of less than 100, it can only use one of the corresponding manuver but if the agility stat is greater than 100, two of the "Sneak Attack" manuvers can be used.

The Battle Tactics FAQ gives a full list of advantages.