Is it permissible for a participant in a Mudarabah company to guarantee another partner's capital in return for receiving 50% of the profits, and to be a partner in profit and loss according to specified percentages (such that he profits 50% of the capital and loses 20% of it in case of loss)?

A valid mudarabah (definition) (profit-sharing) contract has conditions, among them that the share of both parties in the profit must be a common percentage, and that the mudarib (working partner) does not guarantee the capital except in cases of negligence or transgression. If you paid your money for mudarabah under these conditions, then the mudarabah is valid.

As for accepting your friend's money for mudarabah with another mudarib, in addition to the aforementioned conditions, it is stipulated that your friend explicitly permits you to do so or gives you a general authorization.

The condition of guaranteeing the principal capital or part of it is invalid and transforms the transaction into an interest-bearing loan.

The agreed-upon share must be from the profits, not from the capital. You are permitted to guarantee your friend's capital in one specific case, which is if you tell him: "If the first mudarib transgresses or is negligent with your money, then I am a guarantor." This is known as guaranteeing what is not yet due, and it is considered valid by the majority of jurists.