It looks like your on your own. I'd think light would be the big problem.

How come you're warmer and you get more sun in the summer? :( I thought Alaska was chilly.

Tomatoes grow indoors just fine - they're a tender perennial. I had a cherry tomato plant inside for three years before it finally started to decline in production. Given good care and enough light they will last quite a while. You do of course need to cut them back so that they're not 30 feet tall and give the stems a shake to ensure pollination.

In regards to the rust, it's probably some sort of stem rot. I recommend starting indoor plants from seed if you can, rather than bringing ones indoors. Also, a fan set to its lowest setting blowing at the plants after they're about six inches tall will do wonders at keeping them sturdy and hardened off, if you will.