Most of the newer themes are responsive. As for load speed, that’s a lot more about whats on the page and the hosting company then the theme.
If you look at the help guide link above, from 5.3.2 (pre 6) there are steps to follow to convert your project to RW 7.
As for themes, I would take a look at ThemeFlood and [SeyDesign], they have a great selection, and excellent support. Both are owned by Will Woodgate, and he offers free demos on all the themes.
I would probably start with the upgrade process first, and then once you have a project file in the new RW 7 format try some of the themes out. There has been quite a lot of changes from RW 5 to 7, so you’re reasonably going to need to do a bunch of reworking things.