Second question: Are the ballots counted manually at some point for verification purposes?
Third: If on jan 19th it’s found out that the other guy really won, what happens then?
Too late.
The electors will meet to cast their votes in the respective state capitols on the first Monday after the second Wednesday in December (12/17, in this case). The state's count must be complete and certified by that date.
The newly-elected House and Senate will then meet in joint session to count and certify the electoral votes on January 6. Whereupon, the next President is officially elected.
But, as noted, the states must have finished their count by December 17. It is this deadline that was instrumental in SCOTUS instructing the Supreme Court of Florida to knock it off with all the recounts and get down to business in 2000.