Your provider sets quotas. You should ask them what they are. Good maintenance practices are always a good idea. Empty the trash. Make folders to sort your keeper emails into so you keep the Inbox open to receive mail. Decide if you really need to keep every message you receive. Compact your folders on a regular basis. Are you using IMAP? If so, yes if you delete messages on the server they are gone. Read about how IMAP works or you may have a surprise coming. If you move messages to folders under thunderbirds Local Folder account the they are on your computer and not affected by deleting them on the server.