I have noticed that when you put a member into the moderators group, thus, they are moderators but they can't lock/move topics, or moderate them, unless I set the permission of the moderator to admin.

Is there a way to make moderators(the users who are added in the moderators group) be able to lock/move topics without setting their permission to admin or without letting them access the admin panel?

Or Can we add more Permissions in addition to user & admin?

Hello,

Please check permissions in Admin CP > General > Categories & Forums.
Make sure if you allow the mods to moderate?

Yes, but there will be a "Moderator: Moderators" Marked under each forums. I think this has to do with the "User Permissions" & The Groups, when you edit a user. In general, I think moderators should be able to moderate any thread without the "Moderators", marked under each Sub-Forum.

You can remove that text below each forum. The Moderators: Moderators means who can moderate that forum.

In general, I think moderators should be able to moderate any thread without the "Moderators", marked under each Sub-Forum.

Yeah, thats whats happening right now. Are you confused?

Ok, Can I remove the text which have only "Moderators" marked, because there are some sub-forums, where I have put a single member to moderate.(I don't want to remove these one)

Yes => ACP > Display > Structure/Hierarchy > Hierarchy > Display forum moderators : No.