No, you will have to present the Netherlands Visa application yourself along with the submission of biometrics. Hence, it is not possible to send someone else on your behalf for Visa application submission.
If you are applying as a resident of UK, then it is mandatory to acquire travel insurance that will cover at least €30,000 for any kind of medical emergencies in all of the Schengen countries.
The appointment date at the Birmingham Visa Centre depends on availability. However, after the Visa Centre approves your Netherlands visa, it should take 10 to 15 calendar days for your Visa to arrive via courier. So don’t delay to apply the Netherlands visa appointment booking at the last moment.
Extensions are only possible in exceptional cases, like if you are facing any medical emergencies or there is a war or any natural calamities, etc. Remember not to overstay, as it will result in fines, deportation, or a permanent ban from entering Schengen countries.
A normal Netherlands Tourist Visa will only allow you to stay for a maximum of 90 days out of 180 days validity. So logically, if you acquire a job with that Visa, you will have to return, once that Visa expires. For that, you will have to file for a separate work Visa or work permit.