Can I get pregnant if BF had sperm on his hands, then washed with cold water and soap and then put his condom? Can the sperm still be alive??

DOUBT IT. The conditions you describe make transfer of a healthy sperm unlikely.The soap and mechanical effect of washing likely rendered them inactive. That said, in the future make a point of covering up the source before stimulation leads to sperm leakage. It only takes one to do the job. Intercourse before the condom is applied can get you pregnant too.(leakage)