Exciting times ahead.
I had an induction last year. I'm not sure how much of it would be modified for a multiple pregnancy, let alone Covid. I'll try to address all your questions though.
First, how they start you off varies from trust to trust. My own used gel pessaries as a starting point, but now they prefer to use catheter balloon instead.
Monitoring, with the gel pessaries anyway, is every few hours. So you should be free to move around at all other times. However, unless you're in a private room, with Covid, I imagine it'll be very limited. My own induction took place in a 4 bed ward bay, so bear that in mind. Once my waters were broken, and I was on the drip, I was on continuous monitoring until I gave birth.
Inductions don't necessarily take forever, even if the pessaries don't send you into labour. The main aim is to dilate your cervix enough to be able to break your waters. The main concern would be that you are a high risk pregnancy. So they're going to want to ensure they have adequate staffing and the equipment available. There's also SCBU availability to take into account. So unfortunately if things are a bit busy, they'll want to delay you until things quieten down. If your waters break on their own, they'll make space, so don't worry about that.
Pain wise, it was uncomfortable having the gels inserted, and other than the occasional cramp everything was fine. ARM was very, very, very uncomfortable. That was entirely due to needing a second midwife pressing hard on my bump to push the membranes down, so the first midwife could rupture them. Gas and air got me through it though. It wasn't until I was truly in labour that I had pain. I was on the drip though, so it was to be expected. Gas & air and diamorphine got me through it though.
I was already an inpatient, so I didn't need to be called in. I believe they usually try to schedule a morning time for you to come in. But if things are too busy, they might ask you to come in at a later time. Conversely, if there's not much going on, they might call you in early! So yes, it could happen at any time.
Entertainment will be key. I worked on the assumption that it would take a long time, and planned accordingly. Download a few films or TV seasons onto your iPad, take a book or two, puzzle books. Make sure you don't forget pens and a long charger! Unfortunately, as I think movement will be limited, comfort is also going to be vital. Hospital pillows are crap, and there's never enough of them to go around. Bring your own, bring a body pillow. I also had my own fluffy blanket. Ear plugs/headphones to ignore the world are also handy.
I don't have any other children (yet!), but I'm sure your little boy will be just fine. He won't remember this at all in later years, and soon he'll have two siblings to adore. Plus, if my experiences of being looked after by other people while my Mum was in hospital having my younger siblings are anything to go by, he'll be spoilt rotten. 😛
Good luck with everything!