Hmm, the best Mexican I'm aware of in Edinburgh is
Viva Mexico (41 Cockburn (pronounced Coburn) St). Not having eaten Mexican in the US (except at Taco Bells) I don't know how authentic it was - but I enjoyed it greatly. Definitely no chips.
You will be able to buy most of the makings for Mexican food here as well - I regularly buy tortillas, there are various other gubbings available (I tend to make sauces from scratch, so not too sure of what other ready made things are available). It's hard to find cactus over here though.....
September -expect cool, probably wet. But Indian summers do occur - British weather is never predictable.
Hope you enjoy your time there, I graduated from Edinburgh University a few years ago now...