Hi Stripeymummy, it sounds like the drug they will be using for the first part of the induction is something called propress if they plan on leaving it for 24 hours before breaking your waters - this is on a string similar to a tampon so if you start to have contractions they can remove to prevent over stimulating of the uterus. The alternative which I am more familiar with is prostin which is given 6 hours apart, and most women with their first baby have at least 2 and tend not o have their waters broken until the next day; I always tell women to expect the induction process to last a 2-3 days and if it happens quicker (which it certainly can do) then that's a bonus. Unfortunately I think women aren't told enough about induction before they come into hospital so a lot aren't mentally prepared for how long of a haul it can be and that's hard. I'm not sure how propress compares to prostin, but I would definitely have in your head that you are quite likely going to require a second dose of medication used to soften the cervix (it may be after 24 hours of propress they move onto prostin). With prostin some people get into established labour, but the majority will require a drip (some having had no pain at all until this point others having had regular tightenings/cramps).
You will have the epidural in place before the drip is started, and if it is a good epidural (which 8-9 out 10 are) you will feel no pain- so certainly able to concentrate on other things, although if you've had a long couple of days with the first part of the induction you might just want to rest. You might be aware of contractions and you might feel pressure and sometimes still even the urge to push as the baby moves down.
It sounds like they plan on giving you a decent length 'passive second stage' - so that is when your cervix is fully dilated but you aren't pushing, to allow the baby to move down and into a good position with contractions and give you the best chance of pushing your baby out without assistance. This could be 1-3 hours. Even if your epidural isn't a mobile one, so you are unable to get off the bed it is still a very good idea to be mobile on the bed, some women are able to kneel depending on how dense the block is, but even moving from your left side, to right, to sitting up etc can help the baby navigate the pelvis.
It is definitely possible to push a baby out in 30 minutes if they are in a good position and the contractions are good.
Sleepevader, there is no reason you can't be mobile with a syntocinon drip and a CTG monitor on, it just might take a little bit more effort (for you and the midwife!). If you're attatched to the CTG with wires (although there may be telemetric monitors available - so no wires, which is even better) the midwife will not want to be having frequent gaps where you are off the monitor (as this prevents her from interpreting the baby's heart rate accurately) so you will need to stay fairly close to it. Sometimes when you are mobile it can be more difficult to monitor the baby's heartrate, so the midwife may need to reposition the monitor when you move, or she might ask that you avoid a certain position (remember the monitor is on for a reason). If your waters have broken and there is loss of contact on the CTG the midwife might suggest (or you can) putting a fetal scalp electrode on, this is a little clip the goes just under the baby's skin on the scalp (does not cause any harm but depending on how much hair they have you may see a little mark from it when they are born), it allows direct contact with the baby so movement/changing position does not affect the CTG.
Good luck all of you going for induction, my advice - be prepared for a long few days, but try and remember it is only a few days, it won't go on forever and you are going to meet your baby soon! Oh and be as mobile as possible, sleep when you can, eat and drink regularly while you can.