Can a woman get pregnant if the man touched his wet penis and then fingered her?

Other things likely. It is more likely to transmit a sexually transmitted disease than cause pregnancy. So that should be a consideration as well. A condom is a small price to pay, in time and money, to avoid worrying about all the problems not using one can cause. Consider it as necessary as a seat belt..
Unlikely. Very unlikely but possible as sperm are present in "precum". It truly depends on the sperm exposure.