There is a pretty good episode synopsis on the battlestarwiki.
Your questions in order:
1) The ship that did not make the 238th jump was the Olympic Carrier. Why it didn't make the jump at the same time as the rest of the fleet was not explained,. However, it arrived at the jump coordinates 3 hours later. When nuclear alarms went off, indicating armed nuclear weapons were on board, President Roslin and Commander Adama ordered the ship destroyed. Cylons arrived 33 minutes after the Olympic Carrier, indicating that the Cylons were somehow using it to track the fleet.
2)The various ships within the fleet have different FTL capabilities. So the jumps needed to be short in order to not leave the least capable ships behind. Also, IIRC, they needed to reach one destination before they could begin plotting their next. Additionally, the continuous FTL jumps was putting a strain on the engines. After each jump, they calculated their next jump, but waited until it was actually necessary before taking it.
Additionally, the Vipers are not FTL capable, but they were flying patrols to protect the fleet. If the fleet split up, only Gallactica would have had any support from the Vipers, leaving all the other ships more vulnerable.
3) As to why it took the Cylons 33 minutes to find the fleet, episode writer Ron Moore explains:
The truth is, there's no real answer. It's just a random number that felt right when I came up with the idea that our people were under continuous, relentless attack since the end of the pilot. I wanted it to be a short interval, just long enough for them to grab a bite to eat, jump in the shower and maybe try to catch a catnap before dragging themselves back to their duty stations and begin the whole tedious, terrifying ordeal all over again.