Is it possible to save sent mail into a Local Folder on my computer by using Thunderbird?

Yes and it is very simple. From Thunderbird Menu → Edit → Account Settings below the email that you want to alter, you will see the “Copies & Folders” option, once you click that you will see several options appearing on the right. Select “keeping a copy” and on “Sent Folder on” select “Local Folders”. You can do the same for drafts and templates if you wish.