Most starter extract kits come with a 5 gallon pot. 2.5-3 gallons is about all you would want to boil in it. As Dgallo pointed out, its much easier to do a partial boil on a stove and add water to hit your gravity and quickly cool your wort down at the same time.
To answer your 2nd question, you absolutely can do a steep/boil with full volume. I still have a 5 gallon pot but I typically start with 4 gallons. I have to watch my boil like a hawk to avoid a boil over though.
If you do full 60min boils, then you can take Dgallos advice and start with 6-6.5 gallons and run your brew as usual. Your gravity post boil will depend on how vigorous your boil was and humidity. Simply put..if you don’t boil enough off, your gravity will be low.
Since your doing extract, another suggestion would be to start with 5-5.5 gallons, cut your boil time to 30-45 minutes and condense your hop timing. Since extract is condensed wort, your essentially just reheating leftovers. Since you wouldn’t recook leftovers..why do that with extract? You can add a little volume back if to hit your gravity and help cool your wort at the same time.
Of the one recipe I’ve done multiple times, going to a 30 min boil was a nice time saver. It lightened up the SRM and I couldn’t tell a difference in flavor. Granted its a belgian so perhaps something like an IPA might be noticed more.
Give either method a shot and report back your experience. It could help other brewers in the future.