Yes, there are craft beer pubs in Porto and microbreweries from Porto! Particularly, Cerveja Letra was born not far from Porto and later opened a beer garden in Porto; Cervejaria do Carmo has around 50 different types of craft beers, giving more visibility to craft beers from Porto than to internacional brands; Fábrica da Picaria has its own craft beer being brewed on the spot (source).
I don't know about any port flavoured or port related beers but some of the pubs mentioned in the above article also offer selections of port wines as an alternative to a glass of beer.
Some craft beers from Portugal: Burguesa, Letra as above, Passarola, Sovina, Toira. Instead, two common local beers that may be found likely in any shop or bar are Super Bock from Matosinhos and Sagres from Vialonga. Sagres is also dark (preta).
Finally, as in the accepted answer: no. Porter beer is originally British and has nothing to deal with the city of Porto, while port wine inherited his name from the city in its early days in XVII-XVIII century.