Transporters work by breaking down the subject into a matter stream, sending the matter stream from an emitter, and reassembling it on the other end. The TNG Technical Manual steps through an example ship-to-surface beam-down procedure. It also notes that beaming site-to-site (i.e. not starting or ending in the transporter room) consumes twice as much energy as a standard transport, because it's two transports without the reassembly in the middle. It is, however, silent on the matter of pad-to-pad beaming. However, since it's usually done when it's an option, it means that the systems probably interface to share the workload.
Depending on how canon you view the novels, this quote from Star Trek: Worlds in Collision by Judith and Garfield Reeves-Stevens shows that it's for energy saving reasons.
"I know, I know," McCoy complained. "Pad-to-pad transfers use only ten percent of the energy a single-pad beam requires."
In the scene where Kirk goes to see Decker in Engineering, Decker and the engineers are working on the transporter systems.
Decker: I knew it. The transporter sensor was not activated.
[Other background chatter]
Decker: Faulty module.
Scotty: Cleary, put a new backup sensor into the unit.
There's been plenty of time for troubleshooting at this point, since Kirk and Scotty took a fairly leisurely shuttle ride on over, and Kirk's been wandering around the ship a bit before he goes to Engineering.
Because the Enterprise's transporters are on, even though they're malfunctioning, a pad-to-pad transport from Starfleet to the Enterprise is initiated. So the answer to the first part of your question is that they weren't testing the transporters on the new crew; the transporter was not properly disabled at the time. The circuits blew just before the transport of the new crew began, with disastrous results.
I've never been especially happy with the transporter malfunction part of TMP because it raises exactly these questions and more. Starfleet knew that the Enterprise was having transporter trouble. If the Enterprise crew thought the transporter was fixed and put it back into service before discovering that it wasn't, then the safeguards in place are extremely shoddy for something that's supposed to be incredibly safe. If it wasn't fixed but still in service for some reason anyway, then both the automatic safeguards and the engineering procedures are horrendously flawed.
The answer to the second part of your question is probably cynically that they could initiate a pad-to-site transport for Kirk, but Starfleet didn't think about it because the writers wanted to spend fifteen minutes showing the audience how awesome the refitted Enterprise looked.
Storywise, the purpose of the accident was to underscore how unprepared the ship was to tackle V'ger, and also to dispose of Sonak in preparation for Spock's arrival — Leonard Nimoy wasn't originally going to be in the movie, hence Sonak. Still, it's a gruesome and cruel way of handling a pair of characters, particularly since V'ger is scary enough by itself, and everything else going on on the Enterprise already shows how unprepared they are. That Dr. McCoy's fear of the transporter is played for laughs just a few minutes later makes the ship's crew, and the movie, seem needlessly callous.
