Can I use the same COE I used to purchase my current home if I am relocating?
You may be able to restore an entitlement you used in the past to buy another home with a VA direct or VA-backed loan if you meet certain requirements.
Does my current home need to be sold to re-use my COE or can I keep it and use it as a rental property?
You can re-use a COE if you've sold the home you bought with the prior loan and have paid that loan in full among other requirements.  If you wish to request an entitlement restoration, fill out a Request for Certificate of Eligibility VA Form 26-1880 and send it to the VA regional loan center for your state.