In a nutshell it took an extraordinary effort to stop, and they did mention the special crystals decayed rapidly.
The 'three months' was also mentioned (in the starfleet message they were decrypting, as the determined speed to for the crew to get home, so I guess either way, that's supposed to be accurate.
Too fast. The phrase "that would have made sense" is one of about two dozen reasons why I loathe Voyager. Actually STOPPING was never the problem, all they had to do was shut down the drive before the "phase variance" got so large as to collapse the slipstream. Simulations consistently showed that their engine setup could only keep the slipstream stable for about seventeen seconds, after which they started to run into trouble. Voyager was in the slipstream for about a minute and a half at most. Assuming 100 seconds, that would mean they were traveling about 100 light years per second (probably faster, but this is a nice round number). At that same velocity, a fifteen-second slipstream burst would be short enough to ensure controlled entry and exit without the phase variance popping up and would still cover a distance of about 1500 light years. Assuming the engine might require a bit of checking and tuning between bursts -- say, five or six minutes before jumps -- then Voyager would be able to return to Federation space in about four and a half hours (43 consecutive slipstream jumps). They could have easily spaced that out over the course of a whole day -- one slipstream jump every half hour -- and been back on Earth in time for breakfast. Instead, they assumed that their best option was to try and one-shot it to Earth and use some kind of technobabble solution to their shoddy engine design (or multiple solutions; "try inverting the quantum field! Try remodulating the deflector! Try a routing a graviton pulse through the feromactal drive!") instead of simply using the engine as-is and accepting its basic limitations. Which, actually, brings me to an interesting thought: if I were to reinvent the slipstream drive for a TV or movie series and have it be an actual mass-produced engine technology, I'd build that basic limitation into it by default: the slipstream can only remain stable for about fifteen to twenty seconds and requires a couple of minutes of cooldown in between starts; that would basically make it a BSG-style jump engine, but it would be a lot more reasonable from a plot standpoint since the cooldown period might be highly variable (say, if your ship is old or you've been using the engines a lot or if you flew through a stellar nebula on the way here, that might increase the cooldown from 20 minutes to an hour).
No. They had to get not only get to the edge of the Alpha Quad, but then travel on the the edge of the Beta Quad. Earth being at the juction of the Alpha and Beta Quads.
Yes but aren't the quads laid out like this Gamma Delta Alpha Beta So to reach the edge of the Alpha quadrant coming from the Delta quadrant you would have had to be in Beta Quadrant