Is putting it in a west facing location a good idea?
Lots of sun is good for most bonsai provided you can water appropriately. Junipers like sun but they definitely do not like to get totally dry roots. As has been mentioned, all trees develop more compact shoots and smaller leaves when they have more sun. less sun gives longer shoots and larger leaves.
When should I cut it back to produce more compact growth?
Whenever it needs it. I have not noted a time of year that is not good for trimming junipers. Caveats are: don't take huge amounts off at one time and allow the tree some recovery time before hitting it again; and allow time for recovery after repotting before pruning more than a little off junipers.
Some junipers have naturally open growth and nothing you do will make it compact and dense. I'm pretty sure you can do a bit better with this type but it still will never be as dense as a Chinese juniper.
Should I cut or bury the roots around the base?
That depends what else is there. Junipers naturally grow extra roots if the trunk is buried a bit deeper. Some of mine even grow aerial roots from the trunk above ground level if the foliage is dense and soil damp enough. I suspect that's what has happened to this tree while it was in the grow beds wherever it was grown.
There is usually much stronger, older roots just below in which case just cut the upper ones but if you explore and find just 1 large root underneath I would keep the new roots and cover them so they thicken and become the new surface roots.
and am hoping it gets the softer mature leaves.
I suspect you are in for disappointment. Looks like J. procumbens to me and procumbens rarely develops the softer scale foliage.
I am hoping more sun will get it to back bud and be fuller and less leggy on the cascading branches.
Extra sun should help address the open areas but you will need more than just sun to address the bare areas on the cascade. Despite being a prostrate type juniper these are still apically dominant which means the upper parts will always grow better than lower parts. Whenever the top part is allowed to dominate the lower parts will slowly decline. YOU need to balance energy distribution by trimming and thinning much more in the upper sections to convince that tree to invest a few more resources into the lower areas.
That's just one of the facts of life for cascade plantings.
Extra fertiliser may also help this one grow better.
I would also be allowing the tree roots access to the full pot rather than restricting root run. I think you'll get much better results that way.