How long can I keep uncooked fresh squid ink pasta in my fridge? When does it go bad?

Yes, it keeps a long time in the freezer. But I'd decant it from the jar to freeze in small portions, to use as needed. Also, you can get it in small packets, which is really convenient - I've bought them individually, a few at a time, but you can also get a box of 50 here: http://www.despanabrandfoods.com/trade/product-catalog/cured-preserved-seafood/sardines-others

Keep it in the freezer and it won't spoil and it you can cook it from frozen!