@villainousbroodmare as the OP says, this varies massively. Stockholm is considered very stand-offish, like any big city, and the people who are local to Stockholm going back generations will say that it's because of all the "new" people with no roots who don't know how to behave. I'd compare it to what I hear people say about London - no-one talks on the tube etc. My family comes from a completely different part of the country and you couldn't take a step there without people chatting to you. In Stockholm you could live 20 years in a building and barely know your neighbours. Where my family comes from the neighbours might come by to say hello on the first day. It's different, just as the OP says.
People will wave at a toddler I'd say. Unless they're miserable gits, in which case fuck 'em. 
Nobody will ever EVER ask you to join their picnic. Ever. Unless they're Arabs. Unless you somehow become friendly over the course of the beach day like, but you'd still probably be on your own blankets with your own food. Maybe the kids will be offered some of the biscuits back and forth.
I agree with OP that people will not be super likely to help you with a pram etc. and it's absolutely a facet of that Swedish respect for independence. But in modern life this is tainted by an absolute horror (in bigger towns/cities) to Talk To Someone You Don't Know so instead of cheerily asking "will I give you a hand" and accepting a "no thank you I'm fine" (which is respecting independence) they're just bloody rude and don't lift a finger.
In all honesty I think the Bonus Family is quite an accurate description of Stockholm people and life, if you can adjust for the comedic exagerrations!
If you moved to Sweden as an English-speaker you'd have the advantage of being a more high-status sort of foreigner. English is respected as a foreign language (seen as "useful"). But you'll never get far without Swedish, unless you work in such a special niche that you call all the shots. And Swedes have an unpleasant tendency to assume that people with accents or who make small grammatical mistakes don't speak Swedish well enough, so you could get bypassed right there. It'll be a struggle, but less of a one if you're white British compared to Middle Eastern (racism is real). Swedes also are (broad brushstrokes) suspicious of foreign training and experience, and many a well-trained foreign professional (doctor, nurse, lawyer) has been aghast that they have to completely retrain in Sweden, from scratch. This might have gotten better in recent years, I'm not up to date, but I went to Uni 20 years ago with a Bulgarian woman who was having to do her entire degree over again, with not one bit of help in fast-tracking it or anything.
In many big towns/cities it's difficult to get a council flat (houses are very rare, we're talking flats and at most terraced houses which are to an extent seen as flats here). It is common for them simply to be alloted by length of time in the queue. So when you're young with three kids and only 10 years in the queue you can't get the big, more sought after flats. It's a real problem and the divide between those who rent and those who own is increasingly bigger. I rent, and we've never managed to get a place big enough to house us well in an area we actually want to live in. New builds have ridiculous high rents, are thus less sought after and easier to get, but you'll be bled dry obviously. You might also have a consolidated housing queue in a town, with both council-owned property and private landlords. To be in that queue you pay an administrative fee every year, so you pay for the privilege of waiting forever in case something maybe turns up. (Yes, I'm bitter.) That said, the quality of Swedish housing is from an international perspective generally good. I mean the damp problems etc that I read about on Mumsnet would be rare. Housing is ventilated and heated. Your balcony is your own and you can obviously hang laundry there if you bloody want to (the idea that this could be forbidden would be ridiculous here). Apartment buildings have communal laundry rooms with drying facilities.
I know a few British people who have moved here and bought great houses simply from being able to cash in on the high prices in the UK. Uppsala is a big town near me and a house will be at least 5 million SEK, so selling a house in the English SE will obv give you a nice head start there.
I'll stop there, what a bloody essay! Sorry OP 