I managed to have all the sent copied to local SENT folder but incoming mail not copied to the local INBOX folder. I want it to arrive in the IMAP folder and be copied to the local INBOX

i want to have a copy of all the INBOX and the SENT items in a local folder.

I'm not sure what you're trying to achieve. If you want your messages to be local, why are you using IMAP in the first place? POP may be better suited for your needs.

Should I download all to the local folder or download to the IMAP folder and copy to the local folder?

I'd just set up synchronization for INBOX and SENT folders. In Thunderbird speak synchronization means downloading an offline copy of your messages so that they are available in case the connection to the server isn't working or unavailable. https://support.mozilla.org/kb/imap-synchronization

This way you can also easily create backups of your message archive by backing up your Thunderbird profile. https://support.mozilla.org/kb/profiles-where-thunderbird-stores-user-data#w_backing-up-a-profile

Whether this is what you want I don't know.

Thanks

i want my messages to be imap so i can send/read on phone too

But when i send a message i want a copy in the local sent and the imap sent. That works

when I receive a message i want a copy in the local received and the imap received.i do not see the option. I can only copy the received manually from IMAP inbox to local inbox

My laptop is my primary email connection, and I use POP. I set the account in Thunderbird not to remove messages from the server when downloaded but only when past a certain age, I think two weeks or a month, or if I delete them manually, the server removes them. I keep multiple backups of the emails, but all locally.

Then when I access my account from my phone or tablet, I get the last month or so of incoming emails that were good enough for me not to have deleted them. I'm very happy with that setup except for one very minor issue I just posted a question about.

Maybe you could try that method.