1) I played around with Fact Finder to get San Diego county by race at the block level, but I only want city. How do I get the city level only?
In FactFinder2, go Geography > Within state: "California" > Within County: "San Diego" > City or Town: "San Diego city, California"
2) What do I do with the data to get forward in my project? Join it through Access?
It depends on your analyses. In my opinion, it's probably easiest to use Excel.
3) What's the difference in analyzing at the block level versus block group level?
Block Groups are aggregations of blocks. The Census bureau wants to avoid privacy concerns, thus Block-level data for ACS-only questions (formerly Decennial Census long-form) such as median household income are not published. Block Groups are considered large enough to mask this personally identifiable information, so these are the most detailed geography for which ACS data are available.
Fortunately for you, race and ethnicity are in the regular Decennial Census, thus Block-level data are available.
4) Can I get this same data (race and age) from ACS versus AFF?
The American Fact Finder is not a survey or a data source, it's just a warehouse in which Census Bureau data are published. You can get this data from the Decennial Census or from the ACS. If you can choose, go with the Decennial Census, since ACS data are an estimate while the Census is a true count of all persons.