My cousin got e/mail from USCIS that her I-485 (employment based) is approved on 2/24/05 and the approval notice is in mail.My question is
(1)has she become LPR from the date of approval or she will be LPR on the date when her passport is stamped?
(2) She is working with the sponsoring employer on H-1 visa, will she be considered to be working on green card from the date of approval of her I-485 application?

The date a non-immigrant becomes an LPR is when adjudicating officer stamps his/her I-485 with "Approved" stamp. That date might not be the date of an interview or the date you got a stamp in the passport. That date will be on a greencard. From that date on, her H-1 is no longer valid and my guess would be that she'd be considered working on a greencard.

Cheers.