The event's meaning is not the same on this side of the curtain. All but mandatory attendance (sometimes with people literally checking names off a list), officials' speeches and military parades tend to sour the mood somewhat, and, from what I can tell, that memory lingers still. These days, many people just use it as an extra day off.

They don't call it that and don't behave like that, so no. They have anti-NATO, anti-USA and pro-Russia banners (and one pro-China). But there was a march earlier, at another place. I believe the anti-communists were there as well.