Is there a way to search for a player in game? For example, I have a target with seemingly never ending hack potential... is there a way to find him if he is not one of the ten random battle options?

Gam

Second just thought of question... if there is no search engine, is there a Captains Log or Deck Log type thing I am missing that has a hyperlink to vessels that I have attacked?

No.

This is deliberately by design to preserve game balance. Suppose someone could hack you endlessly so that you never accumulated any research points. How long would it take for you to get tired of the game?

If they retaliate against you, they will appear in your ship's log for about a day and you can hack them as long as they're there (longer than just on the battle tab). The longer they keep retaliating, the longer you can attack them.

Keep in mind there is also a set amount of times you can hack someone in a short period of time (like a week?). This is listed on the ship info page on the "actions" tab.

Sorry I don't know the exact times these are active for; someone else will have to answer.

You can disable someone 3 times hack them 5 times and raid them five times in one day. If they disable you or any other offensive action they will stay in your log for you to attack for 2 days.