Can I forward messages from a private channel to my channel? Should the bot be an admin in the source channel? What else do I need for that?

Junction Bot should be an admin in the destination channel only (it can be a public or a private channel) and you need a Standard account. If your source is a private channel, you only need an active working invitation link. Junction Bot does NOT have to be an admin of this channel. The Bot will join the source channel as a common user. Administration of the source channel can’t find out that it’s a bot. If you need more control over this consider the Direct connection. It allows you to forward messages from the source channel without being noticed at all.
Please note that if you are in our support group, an admin of the source channel can find this out. So for communication in a support group, we recommend using an account other than that in the source channel.