You can write a filter that will move messages directly to trash if that is your question. If you're indicating the ability to tick individual messages to be sent to trash prior to retrieval, then then answer is no, but there is a program, mailwasher (free for one account), that does that nicely.

I can filter future mails to be deleted from the server so they don't get delivered to my inbox.

There can always be false positives, and simply deleting messages from the server without a way to review what has been filtered sounds like a bad idea.

Most email providers filter spam on the server and move messages to a spam or junk folder. Whether you'd still see them in Thunderbird depends on your account type.

With POP, you'd never see such a filtered message, but you'd have to login to your account via webmail to check the spam/junk folder on the server.

With IMAP Thunderbird would still download those messages filtered on the server assuming you did subscribe to the spam/junk folder. You'd not see them in your Inbox though.

For those messages not already filtered on the server Thunderbird has built-in junk mail controls. See https://support.mozilla.org/kb/thunderbird-and-junk-spam-messages

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