I have a couple of comments:
1) Unless you are desparate for work, make sure you feel good about your client. If they are pushy and demanding for discounts then 9 times out of 10 they are not going to be worth what you get from them and the stress and headach they cause.
"Do I want to work or not?"
The same is true for those that are asking you to do something that you know is wrong. Better to send them to your competitors then to try and make them happy.
2) As RCRiver say, you need to create a document and I don't think it has to be a contract or be seen by a lawyer. In the document you clearly state what you will do for the project, and you can state what you will not do. The client should get a copy and sign and return it or at least agree in an email that they agree. This allows you to go back and say "Yes, I will do that, but it is in addition to our agreement and I will have to charge you for it.". The document is your proof of your agreement and clears away all doubt and exposes any lies. It really protects you and the client.
3)Sometimes, as in this case, if you know what the client is likely to "really want", you can do something like make the report and then when they ask for it, charge them or at least save yourself the time you needed to go back and do it. (I very much admire your effort in taking the time to do that work, by the way! You deserve only good clients!!!).
4) For my SEO projects, I make it clear what I do, and that is I increase the qualified traffic to the site by between 2-4 times. This is a conservitive promise that I know I can deliver. But I also tell clients that I can get the traffic, but I can't get them customers.
If there are problems with the site like poor design, bad navigation, high prices, and so on, people are just going to leave. So I always include with my site analysis for SEO, some feedback if I think the site can be improved. I don't want to do my best work and then have the client think I suck because no one buys anything.
I am not "responsible" for their sales, but I am "concerned" about their sales and I let them know that.
5)If a client request something, like using keywords for which no one is using to search with, then I may do the work for them, but I make sure they understand that I am not responsible for poor results and highly recommend that they reconsider their request.
6)I ask for payment by check, even if the client is overseas. I ask for about 50% before I do much work, and the rest when I am done. I do take PayPal, and I never considered that someone might make a claim against me. There is no reason why you cannot as a client for references. If you can't tell, ask them who designed their site for example. Then contact the company and see what kind of client they were to work with. You can also search for their email address, name, company name, or phone number in Google and see if you can find out something about them.
I check out everyone that contacts me. Just searching their phone number in Google is enough to find out some things if they are in business.
