Mostly in the topic.

Can you use Stim App and Force Enchance to boost a characteristic ABOVE 6?

Or does the hard cap of 6 during gameplay apply in this situation?

EDIT: Apologise, mistype in the topic. Should read 6

Sure, cybernetics allows it, so I don't see any reason to not allow these kinds of options.

Cybernetics allow you to permanently exceed the cap of 6?

Yes. EoE CRB p. 173, 2nd paragraph, left column, last sentence.