Being a bit vague while stating what work you will do normally is enough for most companies. They know that if they are not happy with your work then get rid of you they will, formal contract or not.
Most times the little bits and pieces about what needs doing will get agreed after the job has being on going for a short while anyway and then it becomes more informal which is good, because then you are 'THE window cleaner' who can be approached.
The thing about 3 copies is simple. Sometimes, like in a club or office the person who decides doesn't always work at that location so the person who asked you for the quote or contract doesn't have to do the copying themselves. If they show the contract/quote to someone then they can say to that person to keep it because they already have a copy. If they are the person who decides, then just say it's in case they need to hand out any copies. It is different. That is my point.
Also, importantly and it happens everytime to us, because they then ask why the 3 copies? It's a good way to get them to remember you because it is so unusual to send 3 copies.
This works especially well when giving quotes. Send 3 copies with a quote works. 2 doesn't and 4 is too many. Don't ask me how it works but it does.
With regards signing anything, don't worry. Your signature is on the letter you sent to them and if they do write back, as oppossed to phoning, someone will sign that letter to you but being realistic, signatures don't mean much and as windows_chepstow basicaly said, a legally binding contract is something else.
Most companies just want something in writing for their records. That's all there is to it but we have to go through some formalities first.