It often helps in any difficult situation to take some time to put yourself in the other person's shoes.
Should I react and say to the other-child to step off because it's disturbing our conversation? Should I rely on what teacher does? What if in my opinion the teacher does not handle that situation properly?
I think telling the teacher how to handle the situation better is fine if and only if it would be perfectly OK if she were welcome to come to your place of employment and tell you how you can improve significantly in your job performance. Seriously. This is her job, and you're on her turf. That you have a child attending that preschool doesn't make it ok to tell someone how to do their job the way you prefer.
I think that correcting a child while their parent - or someone acting in authority over the child (in loco parentis) - is not wise, and often ends badly (whether you see the difficulty it causes or not.) Again, if it would be perfectly OK for an acquaintance to correct your child in front of you at your home, then you're well within your right to correct the little interrupter.
However, you need to understand that, just as your parenting should not be usurped by a relative stranger in your own home, this is her job, her place of employment, her choices on how to run her class. You have no idea if she took the little interrupter aside and spoke to him (a teaching moment) about interrupting.
Should I rely on what teacher does?
Arrival time at any school is a busy time, not a great time to have a discussion with someone in charge of the students. If you have something you want to discuss with the teacher, it is far better to do it after the children leave at the end of the class, or to make an appointment with her to meet a few minutes early to discuss the matter.
You didn't ask about the following, but I can give you two good reasons it's not so stupid.
The teacher comes to me, I ask her question about "the rule in the preschool not to bring own toys" which I think is stupid.
First, if a child brings their own toy, they may feel possessive about it and not share, causing problems. If all toys are there for everyone equally, it is easier to teach about sharing.
Second, if your child's favorite toy breaks while two kids are engaged in a tug-of-war over it, the school does not want to be responsible to replace it. Sounds fair to me to leave precious (and not-so-precious) personal items at home.