It depends on the team they are leading. However, I think it would be nice for Team Leaders to have global moderator permissions. Since you let them lead your team, you should trust to to be able to help out with these permissions.
I think they should. They are the team leader so why not? It helps the other moderators out especially if they are more active and the user has been a member for a long time and is trusted
Generally they lead a specific wing of the staff team. Me, for example: I lead the Editorial Team. I do all the management and officially hire/fire members of the team, as well as evaluate the team daily. They're like a manager in a professional, IRL situation.
Yes, I think TLs should have Global Mod permissions. If you trust someone enough to run part of your staff team, you should trust them enough to moderate.
Generally, forum software requires global moderator permissions to perform certain actions (e.g. changing the amount of forum cash a user has), so I'd say team leaders should probably have global moderator access.
Yes, they do. It can come in handy at times. Provides moderation coverage when a mod isn't available/online (timezones play a part in this). Being a leader of a team is a big responsibility, so it makes sense.
Team Leaders should always have global moderator permissions. If a moderator is not online, or something happens where the TL needs to do something out of their teams area, they need to be able to do so. They might manage the team but they have a bigger role in the rest of the forum as well, so it's only fair they have global moderator permissions.
I think it depends on what the team has that the leader is leading.
If the team has global mod permissions, it makes sense to at least give the leader global mod permissions as well. If the team only has section mod permissions, a leader may or may not need global mod permissions. I think if you are trusting someone to lead your staff team, you might as well have them as a global mod just as an extra set of eyes and hands.
On Foundation, our team leader role - which we call a Manager - is a global mod like the staff team they 'supervise' but also has access to certain areas of the Admin CP related to member management through an 'admin assistant' feature. That lets them approve name changes, edit user accounts, ban users and user IPs, etc. They also have access to our admin (management) forum for discussion above the staff level.
With all that said, not every forum needs a team leader/manager role. We found it necessary because both the other admin and myself were needing to focus on other things beyond staff management and delegating. It's necessary on forums like FP where there are multiple teams and admins can't manage/lead them all. But on discussion/niche forums, a group of staff and a couple admins is usually enough.
In the case of ForumPromotion specifically: definitely. We use Team Leaders as the backbone of our staff organization, moderation, and management. While it does put us at a relatively high number for GMods, they each have specific duties.
On other forums: it's really up to you. You may have a different staff structure that doesn't include Team Leaders at all, like I did on Tune Junkies. We didn't have any sort of "team leader," just Admins and Moderators. In that case, some Mods could have GMod powers, and some not.
It all just depends on what you're trying to do, honestly!