Original birth certificate:
I have never known of a K1 being asked for a proof of US citizenship for a joint sponsor. That is a requirement written in the law for an I-864 Affidavit of Support used for spouse visas and for Adjustment of Status. It is not specified in the Foreign Affairs Manual for your K1 visa. My answer would be you don't need it at all, but if you want to take photocopies anyway, that's up to you.
Tax returns:
A sponsor can show their tax information in two different ways.
A photocopy of the whole tax return with all forms and schedules PLUS a photocopy of the W2. That W2 backs up the income reported on the tax return. Anybody could fill out a fake return so the W2 gives it some validity
A tax return transcript from the IRS. Nothing needed with it because it came from the IRS and they know what you filed and they know what income your employer reported on your W2. So no W2 with transcript.
Oaftobark got a reaction from Howins in London embassy K1 visa interview - checklist