Youth Mobility Scheme

Yes, with very few exceptions (like professional sport). You can work in most jobs and also be self-employed, provided your premises are rented and your equipment does not exceed £5,000 in value.

If you are from Australia, Canada, or New Zealand, you can apply to extend your visa for 1 final year while still in the UK. This must be done before your initial 2-year visa expires.

As long as you are under the age limit on the date you pay your application fee, your visa remains valid and you can enter the UK even if you have since had a birthday.