Yes, and this is often the case. As the person you trust the most is usually appointed as the Executor, they are also usually someone you want to inherit some or all of your Estate.
Yes, it is valid but some aspects of Scots Law are different from the laws in England and Wales. It is wise to get a Solicitor to review your Will and often this may lead to writing a new updated Will under Scots Law.
Anyone over the age of 16 who is mentally capable and is not the spouse of the person writing the Will or is a beneficiary of the Will.
No, the Executor can settle the estate without the need of a lawyer. However, if the Estate is large or complex it is advisable to seek out legal advice from a specialist executry solicitor.