Can you atack with chimera directly after atacking a monster ?

No, the rule is very simple you attack all the monsters on the field or attack directly just once

I know thats how it works, but im curious...i've never actually seen that on any ruling.

exactly - I have never seen this ruling, even in the oficial ude site...

Tsk tsk. You guys put NO effort in looking for rulings, eh?

# "Asura Priest" may attack directly if it has not already attacked a monster this turn.

# "Asura Priest" cannot attack a monster if it has already attacked directly this turn. For example, the opponent activates "Call of the Haunted" or "Scapegoat" after "Asura Priest" has completed a direct attack.

That right there shows that Chimera can NOT attack. Heck, they even have one DIRECTLY for Chimeratech!

If "Chimeratech Overdragon" attacks directly, and then the opponent Special Summons a monster during the same Battle Phase it cannot attack it.

I'm pretty sure I know the answer to this already, but what if you clear their field with Chimera, attack with another monster, and then the opponent summons a monster during the same battle phase? Could Chimera attack it again?

Well, as Xav already stated, all it takes is a little investigating:

It applies for Chimeratech also.