Hi and welcome to Arturia forums.
1. Are all the oscillators modeled with an algorithm based on the original synths, or are they based on samples like IK Multimedia's Syntronik synths?
Arturias V-Collection applications are modeled emulations of the hardware originals.
Only the emulations where the original hardware used samples - CMI, Mellotron and Synclavier - can use samples.
Oscilators are all modeled emulations.
2. Are all the available controls and modulations for the original hardware synth available on its softsynth counterpart, or are the available controls a subset of the original, or unique to the softsynth?
It's not like a sample player where lot's of controls are left out, if that's your question. You can create sounds the same way as in the originals.
Otherwise the answer is a litle mixed. So you'll have to ask more specific.
In most cases the emulations have the old hardware controls and functionality. Some original controls make no sense in a softsynth. In some cases original functionality is left out or not quite the same. New controls and functionality that was'nt in the originals are added, so the applications better can be used in todays context, but you don't have to use this added features if you won't, but just use the applications as you would the original hardware.
I believe there is demo versions you can try out. And you can also download the manuals where there are some informations from the download page. There are also some information on the product sites.
Analog Lab is a extra application, and not a emulation.