Unless it's unlawful for Mormons to discuss these particular details, I'd like to know if proxy baptisms are performed by appointment, or every hour on the hour?

I'd also like to know what kind of info is recorded on the occasion?

Is the name of the baptized party, the party they're being baptized on behalf of, and the exact date and time recoded by some kind of official scribe?

If I had access to the records could I find the exact hour and minute john doe was baptized by proxy in the Salt Lake Temple?

Baptisms for the dead are usually set up by appointment. A local ward will bring over a group of YM/YW and they will each be baptized for 10-20 people or something like that. Each dead person being baptized has a little sheet of paper (blue or pink) with their name and a birth date or death date on it and a witness will check off a little box that says they have been baptized. If you are a member of the church you can go on the new family search and look up your john doe and you should be able to see when and where they had their work done.

I'm not a member yet, so I can't go to the family search sight and look up such info now, but would the exact time (like ten to four p.m. on such and such a date) be recorded?

Does anyone record the time?

I think it is just the date. I am pretty sure you have to be a member to see the temple information. Do you have a particular person in mind?