"My son is the beneficiary, now 19"
"Minor's father is also a beneficiary."
I'm sorry your family is going through this. I'm a little confused by these two statements. So, your son is the adult father beneficiary? And he has a child who is also a beneficiary?
If a beneficiary is over 18 then they are not a minor, they are an adult (even though a will may not allow them to inherit until a later age eg 21 or 25).
"If there is only one executor of an estate and there are minor beneficiaries, and the will does not nominate trustees for those children, is the executor solely responsible for opening and maintaining the trusts?"
That depends.
If the will leaves any gifts to a minor beneficiary absolutely, then there must be at least two trustees (and a maximum of four). If a gift is left to a minor beneficiary contingent on them reaching a certain age (eg 21 or 25 etc) then two trustees are not required.
Minor children cannot give a 'receipt' for any capital they receive from selling a property etc, so it must be a trustee. However, an individual trustee also cannot give a proper receipt in this situation, it must be at least two trustees.
Different circumstances apply to executors, so there can be only one executor.
So, presuming that there is a minor beneficiary and there is no age stipulation in the will (eg must reach the age of 21 or 25 etc) then there must be at least two trustees.
The executor can also be a trustee but will need to appoint a further trustee as well. So the executor will first obtain probate and then, afterwards, appoint any further trustees as necessary.
"An executor cannot appoint a trustee unless the will states this - is this correct?"
No, it isn't. This comes from section 42 of the Administration of Estates Act 1925. This specifically allows an executor to appoint a minimum of two trustees.
When the executor comes to appoint another trustee (or two trustees if the executor doesn't wish to be one) this must be done using a Deed of Appointment which will need to be witnessed etc. You may wish to speak to a solicitor or other professional about how to word this.