Are you allowed to have two personal current accounts with a debit card attached to each one?
Yes, you may have as many current accounts you want, but you should ask why should I have more than one. It is cumbersome and time consuming to keep track of ongoing incoming credits and outgoing debits. Open to bank fraud too, if you aren't careful.
If yes, can a sole trader in the UK use the second personal account for business transactions?
Yes, but no payments to the business. At the end of the year you file you P11D, even if you have a business bank account. You would need to justify the expenses by keeping the bills and stuff. As it will be a personal account, you have to little more careful, not to mix personal and business expenses.
If you are allowed to use a second personal account for business transactions, then why would someone choose to open a business bank account, where you have to pay? What are the benefits?
First of all no company will pay into you personal account, for any transactions, they need to pay you. They will only pay to an account registered with the business, with whom they are dealing with. Benefits are you have your business expenses sorted out in one account and personal expenses in other. Pure business expenses comes out of the business account, rather than from your personal purse, keeps the accounts smooth. No need to sort out expenses at the end of each quarter or at the end of each month.