What happens to my HOPE when I withdraw early?

You will receive 50% instantly and the other 50% is burned

Will the price of HOPE influence the APR of mHope staking?

Yes, following these scenarios:
mHope is equal to the HOPE price for the purposes of APR calculations. An increase in the HOPE price gives a lower APR and modifies mHOPE staking. Also, an increase in the Total Value Locked (TVL) in the staking pool gives lower APR, this is known as pool dilution. Finally, any Increases on the Firebird Finance platform profits give higher APR because there are more profits to be shared.