Negotiable instrument act doubt

No a Drawee cannot become a holder in due course because

'A holder refers to one who has taken the instrument as it passes along in the course of negotiation towards the drawee and not the drawee, who, on the acceptance and payment of the instrument, thereby strips the instrument of all negotiability and reduces it to a mere voucher or proof of payment'

Endorsement to drawee for all practical purposes is treated as full and final settlement of the bill, hence on payment(in good faith) the drawee is released of every liability to every previous holder in due course...

"Can E endorse the Bill to B again"

No, it will be treated as settlement of the bill in full with no further negotiability...