Can you elaborate on this first issue? I can't recreate this right now, so maybe it will be resolved in the next update.

You're free to not use the Twitch log in feature, however do be aware that the only glimpse Twitch Fox gets of your credentials is an access token that can only be used by Twitch Fox and can be revoked by you at any time; it's not like it stores your username and password.

Edit: So, to favorite a channel, you must follow it first. Are your non-favorited followed channels showing up fine? When you say you search for a random channel and favorite it, do you mean you follow it and then favorite it? The distinction is important when I try to investigate the cause of this issue.