BD can't hook into your AJAX login form to post it instead of the internal one. But you can customize that template as you mention above. The template should be copied to your theme directory and then it will be used and preserved on upgrade. More details about that here: http://businessdirectoryplugin.com/support-forum/faq/customizing-bd-to-fit-your-theme/
For your other questions, I need to know a bit more:
- What version of BD are you using?
- Are you running a free or paid listing site?
- Where did you change this image setting?
- Do you have payment plans defined?
Screenshots of these would greatly help narrow down the issue. It sounds like a configuration problem.
For your search issue, the Advanced Search will show all "meta" fields that don't have email validators on them. It will also show a single field for title/long desc/short desc (which will search all for the keywords you enter). Since I can't see what fields you did define, I don't know if they fall outside of those parameters or not. A screenshot of the Manage Form Fields would help me clear up any further questions on that if this doesn't explain everything.