I believe you are already getting the facet values of current data set, so as for your range problem you have to sort the facet value on the client side and supply the min & max values to slider.
This way it resolves your other problem too, because with filters applied, the returned resultant values for facets will change too.
Moreover you can add an additional check for not showing sliders in case facets does n't return anything.
For large data ranges , i think you can use solr stats
eg :
http://localhost:8983/solr/select?q=*:*&stats=true&stats.field=price&rows=0&indent=on
Read here about it : http://wiki.apache.org/solr/StatsComponent