The nice bit is the applications on the EEA series of forms are ..... free!
That is because EEA/EU legislation states that no member state can charge for applications made under community legislation.
Evidence of "durable relationship"? Yes do provide that to help the application. Basically proof that the two of you have lived at the same address as each other, for at least the last two years.
Ability to continue working? Not quite so clear. You have a valid WHV. That continues in force while the application on form EEA2 is considered. So if the WHV allows you to work, yes you can continue working. However ..... :-
It could be argued that under EEA/EU law you already have your Treaty Rights, and merely need a Residence Card stuck into your passport to prove it. As those Treaty Rights certainly allow you to work in the UK, the comment could be that you should indeed continue to work, but against a background of having problems in proving your ability to do so, if for example your existing employer, and certainly a new employer, asks you for proof of ability to work in the UK.
Are you simply hoping to continue in the same employment? Or is there the possibility you might want to change employers in the next few months?