Congratulations. Hope you're recovering ok from the shock. So I'm currently 33 weeks pregnant with twins and may be able to answer some of your questions. I am having non-identical twins. Also a shock for me, as they don't run in the family. (Identical twins is a total fluke and nothing to do with genetics, though, so if you're having them then you probably just got lucky!)
You should expect to have an appointment with the consultant soon; I was booked in for mine asap after my 12w scan, but it may depend on where you live. They will advise you on what you should be taking. it will likely be iron and extra folic acid, and possibly aspirin as well, but I wouldn't start that until they tell you.
You shouldn't need to tell your midwife before your next appointment, but obviously make sure she knows when you see her!
The care path depends on the type of twins you are having and the relative risks – there are a few variants on it, but to simplify, whether they are identical or not. non-identical is the lowest risk type. I have had scans every 4 weeks from 20 weeks onwards; these are primarily to check growth, as twins can sometimes struggle on this score. Identical twins carry more risks and I think you are often scanned every 2 weeks with them. I see the consultant at every scan, but they're mostly just monitoring for growth or other complications, so it's a fairly simple process - I usually see a hospital midwife who does blood pressure, urine samples, bloods as required (at 20 and 28 weeks, if I remember rightly) and then the doctor just pops in afterwards to check everything and discuss any concerns etc.
My hospital have really only just started discussing delivery with me. They seem confident I'll be able to deliver vaginally, based on the position at 32 weeks scan last week. They will be able to identify which twin is lead/presenting based on their positions, and if that twin is breech in the later stages then they'll recommend a C-Sec. if not then you'll have more options. How open they will be to do one if it's not medically necessary depends on the doctor/area, as with any other baby, I think. You are more likely to end up having a C-Sec overall, but quite often that's to do with how the birth goes - any issues with the lead twin can be very dangerous for the second one, so you're probably much more likely to have an unplanned section, and they will recommend that you have an epidural put in early in labour, in case intervention is required.
I can't help on your breastfeeding questions yet, although I understand that it is perfectly possible to breastfeed twins, but to EBF for any length of time I imagine might be challenging. I am intending to attempt mixed feeding, for flexibilty.