If a private seller sells a car is the $$ taxable by the IRS as income? Capitol Gains?

The only "income" reported to the IRS is money earned and then reported against your SS#, such as in a job if you "had" to fill out a W-4, or interest from a bank account - & the bank has your SS# & reports "interest earned." Unless you "volunteer" to include something on the 1040, like money received in a private sale of a car, it is as you said, "private."