Hello and welcome to RTA !

1. Yes your trip looks doable.

2. I would always recommend at least a day a half at GC with time permitting so 2 days would be nice.

3. An intermediate car offers a good compromise between comfort and value but the US is basically geared up to cope with bigger vehicles so you shouldn't have any difficulties adapting. A compact is a little under powered and basic to be comfortable on long runs in general.

4. You would have time to drive through Joshua tree NP if you wanted to detour, maybe pick up a section of old route 66 through Oatman. Lake Havasu, Needles and Kingman are OK for an overnight stop.

5. You should have no concerns the roads are great. Carry some paper maps, drinks and snacks with you and don't let your fuel tank run too low.

You might find that it is cheaper to keep the same car all the way to Phoenix so check it out before renting twice, although that might not be the case if you want the muscle car. Keep in mind that when renting they always state " or similar" so you will not be garuanteed a particular model, just a car in that class or higher if they can' t provide what you booked.