Mogilization is not an instant thing nor a stealthy thing. Before February, most of NATO expected Russia would just try to invade the Donetsk and Luhansk oblasts, instead of attempting to take over the entire country. But that was partly due to the lack of serious preparation. And this partial loss of territory would, back then, have been accepted as no big deal.
If Russia had started to mogilize its troops, then while they're doing that, the other side can prepare as well. So I doubt things would have gone as smoothly for Russia as you think. Besides, one constant of Russian thinking is that they lie to everyone including themselves. They thought they had enough force to take over the entire country, they didn't. If they had mogilized, they would have thought they had enough forces to take over the entire Ukraine + Baltics or whatever. They'd still have come up short because with bigger means come bigger appetite.
Ukraine did mobilise, big time. Had Russia begun in March instead of Sept, they would have finished the war long before now, even if they took 2 months to mobilise. Plus a lot of their equipment would still have been intact, in comparison half of UAF was destroyed before June. And most of the Western stuff was yet to arrive back then, Himars and M777 with Excalibur etc. Bad planning on their part.
Don't get the reference for "mogil".
That's a good idea, they should send 500,000-700,000 Russian troops on very long and very thin invasion columns beelining towards Kyiv, like they did in Spring. The war would indeed get over very quickly; I fully approve of this plan.
Why not? That's how it works. As the main body, a tank division, forges ahead, BTGs take defensive positions along the line and push out. The Russians did it with far too few troops over a very large area in spring, and with the intention of not fighting, which is why they failed.