A) possibly yes, possibly no. A Will does NOT have to be signed by the testator. It can also be signed by someone else in his presence and at his direction. See s9 Wills Act 1837. A Will does not have to be dated.
B) It is not for the beneficiaries to accept. If there is no challenge the appointed executor can apply for probate. There is no "acceptance" required. If the beneficiaries think that there is something wrong - eg the will is invalid or there is a later valid will they can lodge a caveat and prevent probate being granted. In the meantime, there is nothing to stop the executor getting on with things.
C) Technically, if the WIll is valid and appoints an executor the assets vest in the executor immediately following death. An executor does not have to wait for probate. However, practically speaking, most bank accounts will be frozen once they are notified of the death of the deceased and will require a Grant of Probate to be released. Furthermore, if there is a challenge, the executor would be a bit silly to do this.
You may wish to read some similar posts here which give some info:-
http://www.theanswerbank.co.uk/Law/Question1365789.html
http://www.theanswerbank.co.uk/Law/Question1365587.html
I think its about time I went back to work. Clearly there is a lot of this stuff about right now.