1. It's important to specify non-solicitation and buyout options in the contract with the client. This is something you need to put attention of your lawyers to. It will strongly depend on your country, country of your client and the laws of which country you will use in disputable cases.
2. Not sure how it's possible to sign SLA without mentioning the company name. Never saw such cases.
3. Depending on the level of the integration with the client and Agency maturity, the Agency can do pretty much everything - product, project management, UI/UX, QA, requirements... anything you can do yourself, but fail to do because of lack of right specialists.
4. The main reason why you may want to work with the Agency is the quality and expertise of their resources. Price should be always a secondary thing (unless you want to offload some simple things - like manual QA, or data labeling, or something like that). Sometimes Agency can have significantly more expertise then you have. Use it properly - and, of course, find the right Agency. Clutch is a very good data source.