Not an immigration question. Talk to your boyfriend's lawyer.

Can you petition for your mother & father? Yes. Will it take more than 10 years before they can return to the US? Yes

I have a deportation order?

No, you 2 can not 'adjust' to a greencard ... based on the few facts you have stated Talk to your lawyer.

ARC ==> Alien Resident Card ... ie: greencard. Are you sure she is only visiting?

You "read" wrong. Go ahead and see your parents ... keep in mind that you still have US tax obligations.

Yes, it appears that the I-130 is approved and this is a POSITIVE step forward.

As an illegal child (17 y.o.), if I leave the US am I allowed to come back?

Yes, you can leave. You won't have a bar. BUT, your act of overstaying voided any visa you may have in your passport and you might have...

Can I be paid by an USA organization via a W-8 Ben Form while living in the UK and have a green card request in process?

You should be OK ... this form is used for you to verify that you are not a citizen, nor resident of the US ... which is true.

My Ead was lost by postman?

Q:1) does 180 days automatic extension apply to my case as well even though my case was approved but USPS lost it ? If this does not apply then A:...

Do I have to file a renewal form for I-131 and I-765 ?

You have to file ... FAST ... there is no automatic renewal.