Grouchy

I let go and switched to the private program/service.

It defaults to config.hjson. Check the defaults.hjson file for a full list of options including the pool_size variable.

It's in the Lemmy configuration file.

Run your own instance. It's the only way you'll be able to set your own policies. Otherwise you're subject to policies of the instance you're on and those policies may change at any time.

Yes. Synapse is the server side part of Matrix. You install it at a Matrix host, or on a VPS, or even a Raspberry PI device. See https://github.com/matrix-org/synapse#installing-and-configuration

Once up and running you connect a client like Element to it.

Host your own Synapse instance and lock it down to your users.

It sets the maximum number of active sql connections Lemmy will use. Don't set it higher than what your PostgreSQL server is able to handle.

Setup a Koel instance at a host of your choice. Upload your music to it and stream from that. See https://koel.dev/

The setting goes in your Lemmy configuration file. The same place as your database settings.

I don't use docker, so I'm not sure what you need to do there. Sorry.

Sounds like you need to increase pool_size: 5 to a higher number in your Lemmy configuration.

I take the host my own instance path. It's safer and more stable than relying on a third party.