If I wanted to become a mechanic but also be able to have a paratrooper qualification how can I do that

In order to achieve this you would need to train as a Vehicle Mechanic in the REME. https://apply.army.mod.uk/roles/royal-electrical-and-mechanical-engineers/vehicle-mechanic
On completion of training you would require an assignment to a unit that works in 16 Air Assault Brigade Combat Team. Each of the brigade units has a REME detachment that have a number of personnel required to be parachute trained. You must complete P-Company and Basic Parachute Course in order to earn your parachute wings. Service within 16 Brigade is a great aspiration and very achievable if you put in the hard work throughout initial and trade training.