The default export will download the text of all the messages, but it won't download any attached images (it will just have links to them). This tool doesn't export the whole history but it does export the attachments.
I think it might! Despite the Slack interface not showing messages older than 30 days, the official Slack export (even on the free tier) exports all messages. Slackdump might have similar access (didn't try).
It unfortunately does not. I just tried. It only has the last 90 days. You'll need to upgrade, export, then downgrade to get the full history plus the attachments.
We have a free Slack server with 3k members, and buying some better license that’d let us export old messages is like $25k