can harley quinn do any martial arts or h2h combat at all

The most I only see her do is use weapons

Nope.

yes....

She does `gymnastics, but with kicks, not sure if that is martial arts. She doesn't do martial arts she just fights using gymnastics. Just because someone fights in comics doesn't automatically make them a martial artist

No

If memory serves, she's actually a very skilled fighter.

She is pretty skilled.

hand to hand, sure

trained martial arts, nope

I mean, anyone can fight hand to hand but she isn't skilled. Any major villain is gonna be able to handle fodder thugs and such.

she's more of a street fighter

She can probably take on The Riddler. Probably. *cough*

She mostly relies on enhanced acrobatics and weapons.

Skilled combatant =/= Martial artist

she has her own style which is not any known martial arts.

I basically take it that she can take on any nameless character with relative ease. Anyone beneath Robin she can probably take.

Uhh, any evidence that she's a Meta? I mean even Batman isn't considered a meta.

Yes. She is a gymnastics/acrobatics prodigy and also trained for an extended period of time with the furies of Apokalips, going through their boot camp and being among their star pupils. Considering that she also makes a habit of humiliating furies in other comics, her level of skill could be considered to be very high.

Right, right. Is this canon to Nu52?

She knows the ancient art of "BANZAI!"