[bnumair]

what you are trying to do (1 QT and 1 Hospital) would be an ideal situation but for most average reefer is nearly impossible due to many reason. too many complications/cross contaminations, several sets of same tools (as you cannot mix them).
Its a job itself but if u think u can handle it, its a perfect setup.
To answer ur questions:
yes a hospital tank should be setup using shrimp method so its stable all the time and not requiring a lot of water changes and parameter swings. As hospital tank is needed for halfway dead/sick fish its best if water parameters dont change much.
this is all true unless u use copper then story changes. in copper treated tanks water changes will come into play.
Hospital tank once taken down after copper use will take longer to cycle unless cleaned and copper absorbed out of it. you can take the filter in sump approach and keep few handy to restart the hospital tank after taking/cleaning it down when needed.

On the tang for now QT it and watch it over 4-6 weeks for ich (will eliminate your suspicion of sand in a bare bottom tank). if it doesnt appear then ur good after 6 weeks but if it has an outbreak then u will need to either do hypo or copper or tank transfer. If u go with copper then there is a step by step guide how to administer copper based med on my blog and u can get there by clicking blue number under my name.

Note: personally i wouldnt keep multiple tanks. 1 Main and 1 QT.
QT can be switched back and forth between hospital and Qt. Remember QT is only medicated when there is a problem confirmed.