No, all the restriction enzymes have their specific recognition sequence with a defined order, they do not recognize any reversed sequence.

The double stranded example you show would be cut with AflII (or any isoschizomer thereof) creating 5'-TTAA overhangs. Any 5'-GAATTC-3' (or 3'-CTTAAG-5') site would remain uncut.

To my knowledge no.

To the best of my knowledge restriction enzymes will not find sequences by locating them from both directions, but, they typically cut through both strands of any dsDNA. So in your case, given

5'-GATACCTTAAGGTCG-3'

3'-CTATGGAATTCCAGC-5'

If your enzyme cut between the CT for example,  C | TTAAG in the 5' -> 3' direction and had say a 4 nt overhang.

Then you will see                                           GAATT | C in the 3' -> 5' direction.

If looking from the 5' sides of each strand you could say that it cut the same sequence either way. Otherwise no.

Use tools to check your restriction cut sites with your known sequence. Such as 

Restrictionmapper (http://www.restrictionmapper.org/)

Webcutter (http://rna.lundberg.gu.se/cutter2/)

VIRS (http://bis.zju.edu.cn/virs/index.html)