Would it be safe for me to "select all" and then click "Fix"?
Probably, but see the Warning in Help-->Help on this tool-->Help topics-->Registry cleaner. It's safest to select only lines you understand. It's not that hard to improve your understanding.
I suggest you click on the Problem heading in the results list to sort the list into problem type order. For a problem type you understand, select only those lines (using for instance click_hold shift_scroll (if necessary)_shift, then Select-->Select highlighted). Then click the Fix button.
Do the same for the next problem type you understand.
If there are problem types you don't understand, leave them for another day when you have time to do some research. Or ask a question about a specific problem type on this forum.
Would that overburden the program or cause other problems?
Overburden? Probably not. Cause other problems? Theoretically possible.
The answer to the previous question addresses both the "overburden" and "cause other problems" matters.
Will all of the fixed items be backed up?
Yes. Registry Cleaner backs up what it removes or "fixes." If a selected line on the list can not be "fixed," Registry Cleaner removes the corresponding registry item.
