Actually we have all the features that you mention - I posted the links to our job boards in another comment.
Also on mobile there's a few CSS overlapping items, just FYI it hurts the image of the site a lot.
As for the first question: it depends on which country do you target, essentially on each site you can filter to find remote roles and some roles that offer Visa Sponsorship (which is important in case you would like to move to Europe)