I'm guessing you're pretty new to internet marketing and AdWords (my apologies if that was a bad guess).
Most agencies (not all, but most) who play more of a consulting role and don't do everything have a difficult time being successful with an account if the client does not know much about online marketing. Often the savvier the client, the better the agency's results (or the client knows enough not to choose certain agencies based upon interviewing the agency).
I would suggest you finding a book that is internet marketing 101 (just the basics of website design, analytics, SEO, PPC, usability) and read the book. The few hours it will take you to read this will better help you ask the correct questions and choose an agency that fits with your website's direction and positioning.
Here's the answer to your questions:
-Conversion Code Consultation
Most likely setting up Google's conversion code on your site to track conversions.
-Initial Call Setup
Kick off call to walk you through what they do and what you want to advertise for.
Changing bids, ad copy, etc over time.
Setting up image ads which run on AdWords content network.
-Click Fraud Support
If you find (or maybe them) clicks you don't think you should pay for, they will try to help.
-Google Analytics Setup Consultation (in this they have provided basic and advanced. What is advanced google analytics)
Google anaytics is a stastics package that gives you information about your visitors.