Did Chevy make a 1962 Impala ss with a 283

my guess is "Yes" the "SS" has nothing to do with high performance- it was just a trim level-

I have one and it is an SS

What about a 283 with a 4-speed? Was that combination available for the '62 Impala SS?

Yes, the 283/195hp was paired with the 4-speed in the '62 Impala SS, but they were rare and had to be special ordered. Most of the Impala SS models came with either the 327ci (either 250 or 300 hp) or the 409ci (either 380 or 409 hp).