Mail folders copying issues

Hi,

I have been using the apple mail client on both my macbook and iphone for a long time. I have a talktalk email address and a gmail; the gmail is what I give out and it forwards all my emails to the talktalk account. All my organised mail folders are stored in the talktalk account.

Upon recently realising that my return address had been set to talktalk for a long time (and so people were replying to this address), I decided to transition to simply using gmail on my apple client. In the process, I attempted to move my email folders—which are all contained in one folder called "Folders"—into the gmail account. I realise now that this was very stupid, as a simple google search reveals that gmail does not use a folder system at all. The emails seemed to move across fine on my mac client, but logging into gmail in browser showed that gmail had (poorly) attempted to emulate my folders in its "label" system. All the folders appeared fine on my iphone, only containing none of the emails. Not only that, but a few of the folders inside "Folders" (so not at the highest level) were appearing as "Read Only" for some reason, and contained none of the emails they should have. The "Read Only" folders also appeared completely greyed out in my iphone, and I was unable to click on them at all. I then panicked and attempted to move everything back to the talktalk account. This has been largely successful, but the "Read Only" folders still appear this way and contain none of the important emails they used to. Searching on gmail web client for one of the missing emails yields nothing; they don't seem to appear in the "All Mail" box.

My question is: Where have these emails gone? Is this just a glitch from attempting to sync the gmail organisation system with the apple mail client? Is there any way to have folders in my mail app which are synced with labels in gmail? (I would quite like to have my stored messages in gmail rather than talktalk.)

Thank you.