Personally, I have no opinion about baptism being necessary or not but the WTS does:
Also, if one is disfellowshiped, does that require re-baptism? Can they do anything to you that would require re-baptism?
Answer: The WTS has vacillated on this but currently says no pointing to Corinthians where the "disfellowshipped" man was "reinstated" but no mention of being baptized again. Side point: the WTS does not teach that a df'd anointed jw who is "reinstated" is not demoted to the earthly class but is considered anointed still.
What if you wanted to baptize your son or daughter, so you teach them and then baptize them in the Jordan River when you take a family vacation to the Holy Land? Would that baptism be recognized by God according to JW belief?
Answer: The WTS does not allow just any member to baptize someone into the WTS organization; certainly not even baptized jw women. As to baptized male jws (and Bible students prior to 1931), baptism was a little less controlled but records were kept at congregation levels and submitted to headquarters. What happens if there are no baptized male WTS members to perform this (areas where all the members are women or unbaptized men, they wait until someone can perform the baptism). Actually I thought baptism was a ritual for other humans since God supposedly knows what is in our hearts and minds.
Finally, does each baptism have to be fully witnessed by two duly appointed witnesses (small "w")? Where are the forms filled and can you volunteer to be a Baptist...er...Baptizer?
Answer: This does bring up an account that was related on JWN some time ago. A jw was trying to avoid being df'd and realized that no one he knew or knew him had seen him get baptized, there were no pictures, and it had never been recorded on his publisher card. So technically no proof he had been baptized...so he dodged the df bullet.
Those who do the baptism at assemblies/conventions are selected by WT convention personnel (selected by WT representatives). Are forms filled out, maybe, records are kept I'm sure. Maybe some elder or ex-elder can fill in the specifics. I do know that they are all elders in my area.
I have seen someone take down names/congregations of those baptized at the baptism.
In my grandparents day, no questions, just show up with your swimsuit/swimwear and be baptized. Less ceremony.
As to the litany at Matthew 28:19:
The questions asked and answered at the baptism talk supposedly covers that.