1. Yes you are - and you know you are, because you sneak your stuff into their bin
2. The council provide a bin (or several) for each household, they are not supposed to be shared facilities
3. If you only have a weeny amount of rubbish, just tie it in a bag and put it in your own black bin - but don't put the bin out for collection, leave it until your bin is more full.
4. If your neighbours put stuff back on your step which isn't yours, it could be that other people are copying your example - your rubbish isn't identifiable.
It's just not worth standing your ground because, IMO, you are in the wrong. Use your own bin, that's what it's for. I would be highly annoyed if my neighbours put their rubbish in my bin.