The switch problem is definitely dangerous it needs a qualified electrician to look at it urgently. I would call one out and send the landlord the bill.
I am not sure how you deal with the boiler next door problem ,you should be able to look at it and check it , adjust the thermostat and so on any time you need to . The fact that next door leave the windows open is another hint that they are getting 'free' power from you.
Your entire housing situation needs to be looked at, I am far from sure it is even legal to have the heating equipment in another house. Also from what you now say it looks like the heaters you do have are not storage heaters just normal 'on or off' ones, they cost more as they are using full price power.
I would suggest you post another question about the switches and the' next door boiler' problem in the 'Civil ' section of the Answer Bank Law category where some of the AB users with legal training will see it. Give it a title such as 'Urgent Help needed, Dangerous electrics ' so it gets attention.