a few exercise questions

1. When doing shrugs with a barbell, is there any difference in the muscles involved in the movement when using a supinated grip rather than a pronated grip? I ask because it's hard for me to hold the bar, especially when I've done SLDLs, bent-over rows and upright rows before the shrugs.

2. What is a good exercise to do to work the lower abs? I do not have a wall mounted rack or something else to hang from without serious difficulty, and I find it hard to add weight to a leg lift (I do not know if that's the proper name. I am referring to the exercise where one lies on the floor, places his hands on the floor, and lifts his legs.).

There isn't necessarily a difference. But if you're having problems holding onto the bar, maybe you should do some grip work.

There's no such exercise. You can't specifically target 'lower abs'. Just work your abs.

You're confusing 'hip flexors' with 'lower abs'.

Then use a deadlift grip, or use straps...