Not at all surprised you had no luck on the HMRC website - it's a bit hectic if you dont know where to look!
In reply to your questions:
1. You will need to complete a personal tax return for every financial year (6th April to 5th April). The calculated tax on which is payable by the end of the following January. There will be no estimated tax paid upfront.
2. As a sole trader you are operating as a business and not a separate legal entity or company. You will not have a company registraition number.
3. If you have two incomes one will need to be declared as your main income and will be taxed as per your current employment. The second source of income will be taxed under the Basic Rate BR code which is 22%.
4. As a sole trader you can trade under any unique business trading name you wish. This does not need to be registered although you can apply for a trade mark then no one else can use it.
Hope this cleares things up!