Everyone can come up with their own structure and no two airplane purchases are the same. So really there's no "standard", at least that I've seen.
When I help people buy airplanes I generally charge a fee for theoretical discussions ("You want to buy a [insert aircraft type], here are pros and cons, let's talk about your mission, maybe you should also consider [something else]"). That's generally a flat rate. Then if I go to look at an airplane that involves some level of traveling it'll generally be a daily rate plus expenses as appropriate, and I'll include any test flights I perform as part of that. Locally I may just charge an hourly rate. Then for transitioning, same deal - day or hourly rate depending on location, travel, etc.
Assisting with paperwork, title search, etc., again depends. There are companies that handle title search and escrow that are well-oiled machines. Normally what I'd more do is help people in identifying those companies if so desired. Helping with determining appropriate pricing and terms? Yes, that's part of what I do at least, and I think something a buyer's agent should do, although ultimately the decision rests with the buyer.