Thank you for your response. Please see my response/further questions in italic.
Under EEA Regulations, you do not need to lodge the EEA 2 application, as your right to reside is automatic if you are in a durable relationship with an EEA national exercising treaty rights in the UK.
I received a Certificate of Application acknowledging the submission of my application which states that 'at this stage we are unable to confirm your right to work in the United Kingdom'. So this worries me a lot! and it means that your statement doesn't apply if I still don't have the residence card?
I read that new employers can still employ me while the EEA2 application is being processed but they need to employ the Employer Checking Service (link below). But understandably employers are really reluctant to do this because it is a risk for them. Is there anything you think I can do to persuade them or let me know if there is a normal process they could take for cases similar to mine? I feel quite discriminated against since I've been contributing in the UK for 7 years and potential employers even big banks said they can't sponsor me since they don't have a good reason why they should employ me rather than someone from the UK but strangely my firm which is not as big can.
So, you may let the tier 2 application proceed and lodge the EEa2 application later.
Would submitting two applications have any impact on my EEA2 application being cancelled or the decision of the outcome of the application?
As your passport will be required for both applications, you can only submit one of them, not both.
This is not quite right as I'm allowed to request my passports back for urgent reasons which I have. I stated that I need them back to renew my work permit and therefore my employer has all my documents while the EEA2 application is underway. Obviously, the Home Office just posted my passports back without any other response whether I could proceed with the Tier 2 application or not.