I have used Thunderbird to move large quantities of messages from Local to imap. You'll need to ensure that your local folders are indexed properly, and then start with smallish chunks and keep adding more until you get to a comfortable number. The last time I did this I started with about 1000, then 2500, then 5000, and pretty soon I was done. It could take some time, but be patient and try to leave thunderbird alone to do it's work while moving.
My question is: If I'll take an action in my Thunderbird client (such as deleting messages from the Inbox folder), it will effect my default GMail account?
Yes, if you set up the account with IMAP, both will be synchronized. Your Thunderbird client will display every Gmail label as a folder, thus moving messages in a folder means "applying a label" in Gmail. All changes you make are almost instantaneously visible in the web client too.
If I'll delete message XYZ from Thunderbird, I won't see the message in the default GMail web client? (mail.gmail.com)
If you delete a message in Thunderbird, it will be moved to a folder you set (preferably the Gmail Trash folder). Because of that you will still be able to see it in the Gmail web client, under "Trash".
In order to completely delete messages, you will have to clean out the GMail trash, of course.
Though new messages (after the complete setup and integration of Mozilla Thunderbird with GMail), will be completely deleted from my account.
What exactly are you meaning with new messages? Note that there is nothing changing when you use Thunderbird – messages will still land in your inbox.
How can I effect old messages as well?
What do you mean with "effect"? You will be able to see all your messages in the folders once you set up Thunderbird, which means you can always use its search function and batch move/delete messages, et cetera.
For more details about how to set up Thunderbird, see the following pages:
Best Answer
The mozillaZine article Importing folders may contain a possible answer.
It dates from July 2011, but may still pertain.
The steps it describes are the following :
Tools -> ImportExportTools -> import mbox fileA second possible procedure is described in the mozillaZine article Manually importing and exporting, which is basically replacing an existing inbox file with the old one. For that to work you should probably use the same version of Thunderbird that created the mbox.