Hi Abena
Franca has answered all your questions much better than I could. I lived in Milan for 10 years and can vouch for the appalling pollution, unbearable heat and humidity and mammoth mosquitos. Apart from that everything's great . I now live in Monza which is just a short train ride away and miss Milan like crazy.
I have a DD who's 22mo, she was born in Milan and so I've done all the rounds of paeds, consultori, baby groups etc. There aren't really any toddler groups like in the UK, but as soon as you settle in go to the nearest consultorio familiare/pediatrico and get a list of activities near you. There's usually a baby group linked to the consultorio and occasionally there's something set up for children over a year too. Otherwise there are these centres called Tempo per le Famiglie, usually one or 2 in each quartiere, where you can take your toddlers 2 or maybe 3 times a week and meet and chat with other mums. You should be able to find out about these from the consultorio too.
Regarding private nurseries, they usually cost around 650/700 euros a month for a full day. I pay 680 here in Monza for 8-6ish, but that includes all meals and nappies. If you only do until 4pm then it's usually about 100 euros less. The state nurseries are means tested and cost less, but you have to supply all your own nappies although meals are still included.
I can't help you about the formula as I don't know much about it, but it's horrendously expensive here, as are nappies and other baby accoutrements. For nappies there is a factory near Rho (satellite town) where I think you can buy a pack of 56 for 8 euros or something like that. I can find out where it is, never been myself as I use cloth mostly, but a lot of my friends go there so I can ask them.
I hope you enjoy it, It is quite a culture shock but then as you've already lived abroad you shouldn't have much trouble settling in. Plus you're going to be with a lot of ex pats so it should be easier still. Do try to learn Italian, it will make your stay so much more enjoyable and open up a lot of doors, not least if you want to start working here.
Good luck and let me know if you need any more info or help with anything.