1. In my experience, yes.
2. No, all the ARS are different. Maybe you can get overlaps but there is not just one type of ARS for each AI. Capturing an ARS is almost always beneficial, and if the left most option is already unlocked you can hack it for one of the others.
In my game I captured an ARS without scanning and I obtained space tanks. Then I scanned another one and the list shows again exactly the same ships. Capturing it unlocked space tanks again (!) so it was worthless.
I've never experienced this, not sure if its a bug or just unlucky. Were the other options also identical to the first ARS? As that does seem like a bug, or an unlucky coincidence.
3.Yes, through your normal science labs you will find the ships you unlock in the ARS are now alongside your other fleetships ready for higher marks to be researched. Remember you also get an additional 500 knowledge from ARS planets to help facilitate this (though you don't have to).
Also note (Keith if you spot this I think its a bit ambiguous so could due to be fixed) that when you send a science lab to check the ARS ship options they are listed in the ARS tab of the science ship as the MKII variants, this is due to previous versions of AIW giving you both MKI+II ships from an ARS, but is no longer the case. This probably also explains why its greyed out as you may have the MKI unlocked, but not the MKII.