Since you are playing in lag it will be hard to deal with the problems you are coming across. I don't know what problems you are having specifically with Kokoro so I can't really tell you anything. For Hayate's cartwheel kick you have many ways of defending against it. You can parry it, hold it, SS, or throw punish it if it is free cancelled. The low sweep cannot be delayed as much as it was in DOA4, so if it doesn't come right after the mid kick, throw him. But since you are playing in lag you really can't properly deal with that setup that is being done to you.
For Brad Wong it will be difficult to hit him in his laying down stance but you have moves to get him out of it. 2P, 9K, 1P, 66F+K (use this only at range when approaching him on the ground), she has other lows that will hit him but you want to stick to quick moves. You will get counter blown (launched) being too slow to hit him out of it, so be aware of that.
Unless the mid is a true mid you are not going to pick Brad Wong up off the ground from his laying down stance.
If you have anymore questions on character match-ups, ask in the character match up thread:
http://www.freestepdodge.com/threads/you-cant-defeat-me-kasumi.1326/