Filming timespan of Jeopardy!

To answer your questions, I'm going to use this site, Jeopardy-FAQs.com, which is an unaffiliated Jeopardy! site that seems to have some specific knowledge of how the show is taped... perhaps someone who worked on the show.

They shoot an entire week of show in one day, so five episodes per day, and they apparently shoot two weeks-worth of episodes in each week:

Q: I thought a weeks worth of shows were done in one day. Is that the case?
A: We taped twice a week, five shows a day, five weeks a month, nine months a year. Normally the shows you see on TV were taped about two months in advance. There are variances, times off for remote tapings, and breaks for holiday weeks and what not, so no there are not 54 weeks of shows and yes there are re-runs. But Jeopardy! is the "game show" with the most original programming each year.'

And, as a corollary, as an audience member, you get to hang out while they shoot more than one episode. Each batch of tickets is good for the morning taping or the afternoon taping, of three and two episodes, respectively.

In regards to the tickets, there are two audiences a day, the first will watch three tapings, then there is a lunch break for the crew, and the second will watch the last two.

Apparently each episode takes about 45 minutes to shoot, which is then cut down to the final 22-minute episode, likely removing slow pauses between questions that would make the TV version seem to drag:

Q: The show seems to be super fast paced. Is it roughly real time? Or is there lots of splicing? How long does a 30 minute show take to tape?
A: A 30 minute show if gone smoothly will take about 40-45 minutes. Its pretty well oiled. Not a lot of editing is necessary.

There's no specific info on this page regarding whether they pause for the full length of the commercial break but, considering the fact it takes 45 minutes to film the episode, I doubt they need to pause for a specific amount of time... though they likely do pause for a few just to give Alex and the players a break.

As with many (if not all) game shows, I believe you'll find that Jeopardy! has a small disclaimer to the effect of

Portions of this program not effecting the outcome may have been edited.
^{(not sure on exact Jeopardy! phrasing)}

This is very much the case. Pretty much every game show will have to edit out small issues with question pronunciation, audience "participation", or technical errors. As I've already mentioned, the taping for each episode takes about 45 minutes and there are several cases when parts of the show are edited or re-shot. As an example, if the audience yells out an answer, they may have to exclude the question and replace it with an alternate:

Q: What's the procedure if [the audience yells out an answer]? Would that be cut out of the final edit, and how would that affect the scoring?
A: Well the few times I heard it, it luckily wasn't loud enough to be heard by the contestants, just the judges table which is right in front of the audience, so no action was taken. But if it was loud enough to be heard by a contestant, the show would be stopped, the question would be thrown out, replaced and replayed.

Additionally, when Alex has to go to the judges for their opinion on an answer, that "instant" response generally takes 1-2 minutes to come back... and up to 30 minutes.

Q: When Trebek consults "judges", what's really happening (overturning answers, etc.)
A: The judges' table has about ten people sitting at it, including the producers, writers, researchers and a lawyer. If the contestant gives and answer that wasn't the correct response but could be technically correct, he would consult the judges, who then have to research the answer to see if it's acceptable. Or if the contestant mispronounces his response and it needs to be reviewed in the booth. Sometimes this process takes a minute but it's taken up to half an hour.

Q: I've never seen this happen. Do they go to commercial break, or do they edit it to make it seem like the judges instantly know if the answer is acceptable? Every time I've seen him ask the judges, it seems so instant.
A: It varies, sometimes the rulings are instant, sometimes they need to stop taping and it takes anywhere from 1-30 minutes. Editing is done at that point.

And from a personal account from a Jeopardy! contestant, Terri Pous:

Not everything is as it seems on TV. Alex stumbles over his words, the board malfunctions, people contest answers — you name it, it happens. It's TV! Through the magic of editing, none of this is visible to home audiences. All of these things happened on my episodes, in addition to some awkward pauses during the interviews, and 10- to 15-minute breaks in which the review board debated some answers. The day before, Alex had swapped the interview questions! It's fun to see it all happen. In addition, the clues stay in those small boxes on the board, which made them hard to read from the podium — I found myself hunched over and squinting a lot.

Since the question was initially more broad, I thought I'd add some other info.

When I was in high school, I was on a game show called Click that was produced by Merv Griffin productions (and hosted by Ryan Seacrest). It was shot in front of a live audience. Some of the info below is from my personal experience on that show.

On Click, they seemed to time the "commercial breaks" to allow the tape to keep rolling and we were counted back in as if we were on live TV (which we weren't).

In regards to editing, there was a point in time where one of the competing teams was running on the stage and knocked over the main podium as the clock ticked down to zero. They actually had the team re-shoot their final run towards the podium so that they could avoid showing it tipping over.

And, like on Jeopardy!, they shot several episodes in one day, and shot the entire season in a week or two.

^{Portions of the quotes not affecting their content may have been edited}