No, it hasn't . The 1st Gen RoundUp Ready soybean trait patent expired in 2015 (two is not "many"), and most commercial volume has moved to product using the still-under-patent RoundUp Ready 2 Yield trait (such as RoundUp Ready 2 Xtend seeds, which also have another herbicide resistance trait.)
That said, I'm pretty sure the "RoundUp Ready 2 Yield trait" has nothing to do with the application of RoundUp. It is the same gene that gave resistance to RoundUp but when inserted into a different location it caused the soybeans to add another bean per pod, increasing yield. I don't believe any RoundUp application is required although it usually is since it is normally paired with the original trait.
And you'd be wrong from what I can tell; RoundUp Ready 2 Yield is a trait that provides glyphosate-resistance without (or maybe with less of) the yield cost of 1st Gen RoundUp Ready.
> I don't believe any RoundUp application is required
RoundUp application isn't required for growing any RoundUp Ready crop, but you wouldn't choose a herbicide-resistant crop (especially with a yield cost) if you weren't going to use a herbicide it provides resistance to.
> it is normally paired with the original trait.
No, it is itself a new glyphosate-resistance trait; it's usually paired with an additional herbicide-resistance trait in RoundUp Ready 2 Xtend seeds.
They do. I can't find any free sources with hard numbers, but numerous reports indicate that Monsanto is the top producer and the top four together have over 50% share, so Monsanto has no less (and probably substantially more) than 12.5% of the global market.
In addition, the global glyphosate market growth in the last two decades has largely been driven by another set of Monsanto products, "RoundUp Ready" (RoundUp is Monsanto's glyphosate-based herbicide product) glyphosate-resistant transgenic crops. So Monsanto not only has a large share of the glyphosate market, it also sells the products that are driving most of the glyphosate market.