If a bowler takes the wicket of a batsman, then after that can the bowling side's captain or the bowler call the batsman back on the field to play again?
This is possible, and has indeed happened (at least) once in a Test match, where the India Captain,Gundappa Viswanath, recalled the England Wicketkeeper Bob Taylor.
...umpire Hanumantha Rao upheld an appeal against Taylor for a catch behind the wicket, off Kapil Dev. Taylor hesitated and protested at the decision. Viswanath, the Indian captain, who was fielding at first slip, was as certain as the batsman that there had been no contact and persuaded the umpire to rescind his verdict.
Viswanath was a successful batsman in the India side in the 1970s, but only captained two Test matches. His cricinfo profile suggests that this was typical of his manner:
He played the game in its true spirit: a century had little value to him if it didn't contribute to the team cause and he disputed an umpire¹s decision only once, recalling Bob Taylor in the Golden Jubilee match against England in 1979-80. It cost him the Test, one of only two where he led India, but to Vishy, it mattered more that the game should be played fair.
Yes, a captain can withdraw an appeal should he decide to. See Law 27 section 8. He must have the agreement of the relevant umpire, and it must take place immediately after the fall of wicket.