My first thoughts without reading all the replies were-
If you plan on autocrossing it you'll likely get some flack from the rule nazis that call it a race car rather than a street car. It's got no "stock appearing" interior, lexan windows, a modified floor, narrowed frame rails, etc etc. This puts you in a class competing with purpose built full custom frame autocross race cars, and to be competitive there it costs a lot of money and you have to have your ducks in a row with engineering the suspension.
Are the window regulators still in the doors - if you put glass back in will they roll up and down? More than likely they left with the original glass.
It's a drag car, realistically you'll completely replace the entire suspension and brakes to make it handle well/ stop.
Tire spin can be controlled with properly setting up the suspension. How often have we seen Elkys lifting tires at the drag strip, and there are a few elkys doing well in autocross. Any car, even a 69 Camaro, can get oversteer and kick the rear out if there's too much power and/or the suspension is set up wrong.
Those are big meats out back. Wide street tires that are sticky enough to be competitive on the autocross course are hard to come by, the Rival has a 335-18 but that's not going to fill those wheel tubs. Just guessing on the rear axle width, rear wheels with that much offset to make a 335 work on that axle may not be cheap and all the weight will be on the outside of the wheel with minimal backspacing. Not sure that's the right combo so you may be looking at a new rear axle?
With narrowed frame rails will all your new suspension pick up points be at optimum for handling?
Old fiberglass has a tendency to sag, so panel fitment may not be the best if you're looking to have a pretty car.
In a way, it would almost be better to start fresh with a full bodied car rather than starting with a "cut up" old school built drag car, but that's an opinion and not necessarily fact.
Lighter weight is an advantage, and you might be able to sell all the drag suspension out of it.
I bring all this up because I have a drag Nova that I was toying with turning into an autocross car. After thinking about it it was way too much backing up to move forward and decided to leave it a drag car and just autocross my daily driver wagon.