Stay to the right until it's clear and then cut over. Don't cut over until there is a shoulder to go to. Better yet, stay off limited access highways. It's a lot more enjoyable.
Easily. You might want to consider the adventure cycling route network. I can think of a few places on ACA routes I have done were you had to be on the freeway for a stretch, but I would guess it is less than 1% of the distance.
Yeah, I think there was only one section (I-80 East of Rawlins) on The Trans America where we rode on interstate. I don't recall how long it was, but it wasn't all that far.
On the Southern Tier I rode a lot of interstate and didn't mind it. In fact I rode quite a bit more interstate than the official AC route uses.
It is easy enough to navigate the interchanges if traffic isn't crazy heavy and it isn't a really major interchange, like where you need to cross multiple lanes of traffic. Those can generally be avoided though.
If you aren't comfortable crossing the exit lane, you can typically just exit and then get back on via the on ramp.