Cutting administration achieves these goals. (It's not the skyrocketing number of tenured professors that is driving college costs.)
Now, do you have to cut research in order to cut administration? Research takes a lot of administration, but that should be paid for by the research, not by the students.
No. Indirect costs on grants aren't some slush fund used to fund whatever but are real costs involved in doing science. It costs money to build lab facilities, maintain and repair lab equipment, pay salaries of support staff like IT folks and lab techs. If indirect costs get capped, more of the actual grant will have be used for these things and less science will get done.
