Of course, we only have one side of this story so I feel the need to play devil's advocate a bit here.
If the building materials had been there for a while and appeared to be surplus to requirements then they might have thought that by taking them off your hands they would be doing you a favour. With the skip, they didn't just put stuff in it - they asked you, so the neighbourly answer should surely have been that if there was space when you had finished, of course they could have it. (A real CF would just have dumped stuff in it when you weren't around!)
Asking about services and contractors? - well advice is quick and easy and costs nothing - you are obviously doing a lot in your house and probably have a head start on them and recommendations are always better than random choices.
Your husbands jobs - you said it was a shared gate, so that is for your benefit too (so why mention it?) and the solar panels - is this a major thing or just a five minute fix? If it's just knocking in a few nails for example and your husband is handy with a hammer, then what's the problem? They are probably not fit enough to do it themselves anymore if they are elderly and yes, they could ask their kids, but if your husband is already on the scene with his hammer, then why not just ask - he could always have said no. If they had, in conversation, said to you that their solar panels needed a nail knocking in and their son was coming next week to do it, your husband would probably have offered anyway! (I am assuming it is only a minor job otherwise it would require a professional).
The thing that I do find very odd however is the coming into your garden uninvited - What is all that about? I think your husband might have to apply his DIY skills to building some sort of gate as his next job (or - an idea from another thread on here - tell them that you are naturists and therefore need privacy in your garden! - that should stop them in their tracks!)
A new house is always stressful and I suspect that if their house is also new to them they are feeling stressed too so try to be kind - they could just be lonely and looking for friendship.
I hope you get everything sorted and can find a way to have a good relationship with your new neighbours