I feel bad for your predicament. Unfortunately this happens all too often in our Mooney world. It shouldn't but it does. From lack of understanding on both parties part, problems arise that should have been cleared up before the work starts.
First lets look at what really needs to happen
#1 is an " ANNUAL INSPECTION" This is outlined specifically in Mooney's Annual and 100 hr Inspection form (a 100 hr and an Annual inspection in reality includes the exact same scope of items for inspection. If you are renting your airplane then you have to do 100 hr inspections, the scope every 100 hr is exactly the same as an annual inspection.). There is some "servicing" included in the form (oil change , filter change, etc). One needs to verify what EXACTLY is included in the quoted "Annual Inspection Fee". Only the "open up and look and see" portion or also the "servicing" included in the Inspection form.
#2 would be any "servicing" not included in the quoted fee. Wheel bearings, spark plugs, etc.
#3 Fixing or repairing items found during the Inspection (any "Inspection" will include a listing of squawks found during the Inspection)
Be aware that any first time look at an unknown airplane MAY find items not done correctly by someone else. I have seen this in many, many airplanes that I have looked at and it has been discussed in several threads here on this forum. I found a starter power cable on my own Mooney that was replaced with an automotive wire while doing my pre-buy inspection. No info on who did it.
One requisite of an annual and your AI is that he is required to certify that the airplane meets its Type Certificate OR is repaired or modified in an Approved manner. "Subjective" airworthiness really shouldn't enter the discussion. It's either correct or it's not. There is even an FAR that governs 'Inoperative Equipment". You say your ADF doesn't work? How about your autopilot or something else? If it's not inop'd or fixed according to the FAR you could find yourself on the back side of an FAA investigation. If your AI signes it off in that condition, he could too. Yes, I know, I'm a hard a^% on this but, trust me, you don't ever want to be on the back side of an FAA investigation even if they say they are "kindler and gentler" now.
The Inspection fee should also include the AD search BUT if your log books are a mess they may charge more time for research.
Additionally, "inspection time" before the "annual inspection" seems somewhat dubious. What would be inspected that wasn't looked at on the actual Annual Inspection?
As you can see there are at least 3 components to an Annual Inspection. To just say, "do my annual" and not confirm what that includes leads to many misunderstandings in the end.
I do hope you get things cleared up and go enjoy your airplane.