Meeting Settings

PaigeFarrell Here are my responses to your questions -

Is there a way to control who can start a scheduled meeting? This is not possible in meetings except in Live Events via Global (Org-wide default) policy in the Microsoft Teams Admins center, however Customized policies can be created by your Microsoft 365 Administrator - https://docs.microsoft.com/en-US/microsoftteams/meeting-policies-in-teams?WT.mc_id=TeamsAdminCenterCSH

Is there a way to block people from using the chat feature unless you allow it? This is tricky at this point, yet again your Microsoft 365 Administrator can turn chat off for all students , there is no feature that allows for putting off and on of chat by team owners

https://docs.microsoft.com/en-us/microsoftteams/messaging-policies-in-teams

On your last question, we might start a uservoice on adding this feature in the Manage Team > Settings > Member permission area 

https://edudownloads.azureedge.net/msdownloads/MicrosoftTeamsforEducation_QuickGuide_EN-US.pdf  - Follow the link for more settings you might find helpful.