I'm hoping somebody who has a better understanding of Schnorr signatures than me could answer this question. I have a basic understanding of EC math but have not studied Schnorr in great detail.

As I understand, Schnorr signatures as implemented in Taproot allow a script to be created which requires a m-of-n threshold signature in order to be spent.

My question is: is it possible for a completely non-interactive locking of funds? i.e. scriptPubKey. Of course this is is possible with traditional scripted threshold signatures, but as I understand Schnorr signatures requires the signatories to choose random numbers to add to their public keys before a master public key is created. Without these random numbers there is an attack that can be performed by adding the public keys together. Several questions arise from this:

1. Is it possible to choose these random numbers in a pseudo-random, deterministic way, yet still be safe?
2. Do the signatories need to remember the random numbers in order to create the Schnorr signatures at time of unlocking?

Apologies for my really poor understanding of Schnorr. I'm in the process of learning about it.

I appreciate if anybody could help me with this question.