How does the sender know the receiver's public keys in a m-of-n transaction?
Any address that a spender will send to is provided by the receiver. As the owner of the address, the receiver knows these details and will be able to provide the correct sending instructions to the spender. This holds true even for the outdated original multisig construction that required the spender to know the pubkeys, but today most multisig transactions actually make use of pay-to-script-hash (p2sh), so the receiver would simply provide a standard p2sh address to the spender.