Custom plugins are in the works I think.
Compared to other server hosts, Minehut is the best free one out there in my opinion.
And like @BanditEagle said, Use /dl <world/log> to download a world or the latest log file.
I recommend using the /ul world command so something like /ul world dreamsmp downloadLink
You might also need to change the default world name after uploading it because uploaded worlds are usually prefixed with ul_
This kind of thing sounds like it might need web requests, I'm not a professional or expert or anything so take what I say with a grain of salt.
As far as I'm aware web requests aren't fully possible on Minehut as of this time.