Old man with old car, new here with questions

We'll I did the dumb old guy thing and purchased a car off a site without looking. 550 miles away so I took a chance.

I am determined to fix it. It is a 1960 Valiant 170 cu in, automatic, 4 door. Speedo states 97,000 Mi. I have it running and driving. The car has 4 very new Michelins, newer alternator and new brake parts in the trunk. There are photos of the carburetor and one of the car attached.
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Questions to which I have not found answers: 1) Did the 1960 BBS 2901s carburetor have a pull off valve? 2) Are ANY Carter cars usable to retrofit that unit? 3) the car sways on the road like a boat in water with waves. What was the primary cause?

I still have a lot to do on the car but with some helpful input from you folks I will get it done.

Thank you, Hank

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