I will try to reply as best I am able. See below.
It may be an unfair question, in that it forces you to consider your priest in an unfavorable light at least in theory.
If someone entered your parish and declared that they are of the Metropolia jurisdiction, would you say that they shouldn't have communion in your church?
I wouldn't presume to tell them anything of the sort. I am not a priest. However, I would suspect that my priest would not commune them, because their hierarch has broken communion with our hierarch. That much is a given. Frankly, I would be surprised if an Old Calendarist they wanted to commune in my parish, which is in communion with the ancient patriarchates. If they did, they would probably need to be received into our communion. Since they share so much in common with it already, this may be by chrismation or maybe just by confession. I don't know. How that would be done would be up to the bishop and his delegate, the priest.
I think people are attracted to those parishes out of a desire to be more serious. Maybe they have some experiences, like being told they are too devoted to saints, or maybe they confess too much, who knows.
I have no idea. The people here who are in Old Calendarist parishes could probably tell you why they are there. It would be interesting to hear.
In the Russian church here, people spend a lot of time kissing the icons. I don't know how they'd do that with pews in the way, but of course the argument would be, if they're wandering around they're not paying attention! But they are.
Do you mean when they come into the church, or are they wandering around during the Liturgy? Or are they doing this during the Hours? There are certain times during the Divine Liturgy when a person is not supposed to be wandering around the church, period. A lot of our people have a bad habit of coming into church late. But when they do, they still go up and venerate the icons, place a candle, etc., and this is fine, although if the priest is in a procession, reading the Gospel, giving a sermon, etc., they should wait outside the doors to the Nave before they come in. But the priests I've known are just glad to see these people show up and usually wave them in with a wave of the hand. If they are chronic latecomers, that situation might be addressed privately. And these are churches with pews.
They are devoted and are paying a lot of attention.
Wonderful! But I wouldn't purport to judge them. I find that I have enough trouble paying attention myself. Sometimes venerating an icon brings me closer to God but other times, depending on my frame of mind, it can be a distraction or even prideful. I have enough trouble worrying about my own frame of mind. I presume my fellow worshippers are doing the same, and I leave them to it.
To some extent, the interiorization of the analysis can be turned on its head in the following way. The faithful coming in from the Metropolia (or some other TO) would obviously have a good life of piety, being constantly nurtured in the traditional way.
I wouldn't presume to judge. They could be the most pious people in the world, walking saints, or they could be legalistic Pharisees. It would depend upon the state of their soul. Not my call.
But the tendency would be to say, "You're schismatic, no communion for you here."
No, the tendency would be for our priests to say, I can't judge you. But you are under the care of a bishop who is not in communion with my bishop. If you wish to receive communion here, you must first come under the care of a bishop who is either my bishop or is in communion with my bishop.
And thus would end even the conversation, because people are very cliquish, in religion especially.
Not if the person wished to come into the pastoral care of that congregation. That's what communion is. Expressing entire belief with the doctrines of the Church as expressed by that local bishop whose deputy, a priest, is serving that congregation. I wouldn't want to go up for communion in an Old Calendarist parish because my bishop, under whose care I am, doesn't agree with everything that their bishops teach, although I would never say that those bishops or people are not holy or that I will see heaven before they do. Far from it. There are some instances, such as with the Oriental Orthodox, where I wish I could go to communion there, because I believe that we hold the same faith, but because my bishop has not consented to this, I must obey my bishop.
So yes, we should look to see where there is faith and piety, but we prioritize concerns that are harder than that, which are the concerns I'm getting at. I don't want to get part-way in and discover that it's RCIA all over again.
I can't speak to your latter concerns without specifics.