4 - Is it possible to retro fit a conventional stainless steel kitchen sink with an undermount sink? I have a granite counter top surrounding the 2 sinks. Can this be done and if so, is this a major undertaking?

This might work but it will be very messy and probably not give you the best results. First of all, your top mount sink was most likely caulked around the edge, between the sink lip and the granite surface. When you lift the sink, you will see a caulking stain that will most likely be impossible to remove because it has been there for a long time.
Secondly, a fabricator will have to re-cut and polish the opening to the fit the new undermount sink. A topmount sink cut-out is usually larger than an undermount polished cutout so we doubt you will find a large enough undermount sink that will allow you to do what you want.
If you want to pursue this further, start by measuring the already cut opening in the existing countertop. You might have to get under the sink to measure how and where it was cut. Then look for an undermount sink that is bigger than the opening and still fits within your cabinet size. If you pass these two hurdles, go ahead and pull the sink up to see how bad the caulking stain is.

5 - What is European finish?

It is the rich, deep, satin smooth finish rather than a surface gloss. The exquisite European Polish is formed by circular patterns, rather than straight line polishing.

6 - Can I use a rubber mat inside my sink?

No. Rubber mats trap water causing iron deposits, and surface discoloration.

7 - What does the gauge of stainless steel mean?

It is the thickness of the stainless steel sheet used. The lower the number of the gauge, the thicker the stainless steel. High quality residential kitchen sinks are usually 18 gauge (1.2mm).

8 - What is the difference between an undermount and a topmount (inset) sink?

A topmount sink has a lip that folds over the countertop, and rests on top of the countertop cut-out, while an undermount sink is securely installed from under the counter with fasteners. Undermount sinks expose a polished edge of granite, or marble along the cut-outs, and require more polishing, and labor. Undermount sink cut-out is therefore a more expensive option.

9 - Why is my stainless steel sink undercoated?

It is undercoated in order to absorb sound, protect against condensation, and maintain sink water temperature.

10 - Are there different types of stainless steel for sinks?

Yes. Material content, and quality changes from one type of stainless steel, to another. Some stainless steel sinks look bright, and shiny at first, but rust and corrode in time. Corrosion resistance, and durability strictly depends on the best combination of chromium, and nickel content.