Can I ask a silly question please... which is it that you want.. your heading suggests that you want people entering domain.com to arrive at www.domain.com With all the hosting outfits I use that is just what happens.
Your message though talks of wanting .domain.com to work and take you to www.domain.com - that doesn't work on my sites. I can set them up to work with anything.domain.com with no bother though. I don't get the wish to want just plain .domain.com to work... who would enter that.
Not found picture means there is a directory error or something, as for the rest I am more than convinced it's a server / backed issue or an issue with domain settings etc...
I am by no means staff or anything like that, a customer - like yourself, but I will gladly take a look if you wish and need a hand? More than willing to lend a hand....
Trust needs to be mutual, but it's nothing I've not done before... I daren't think of the amount of data and people's details I have seen over the years'
Failing that, submit a ticket??
You claim you have tried every solution posted on this forum over the years and none of them work.
In which case I would suggest contacting your host for support as it could be a server (mis)configuration issue.
Regarding the logo, I have just checked your site and the file does not exist on the server in the location you have specified.