Does porphyria affect my liver? Should I have liver tests?

Yes. Acute intermittent porphyria can affect the liver. You should talk to your doctor about what monitoring is recommended.
Porphyrias and liver. These conditions mainly affect kidney. However flares can be complicated by gallstones. I would assume that ever diagnosed the condition is making sure that all chemistry panels are staying with in desired range.
More than one type. There is more than once type of porphyria and you should let your doctor decide the tests. See this site for more info.