*Not* very Montessori
You can link to a typical day here:typical day in a Children's House
As far as "you haven't been shown that" I must say that I have seen this before but it shocks me. Our trainer (AMI) said that if a child shows interest in something they haven't been shown we should:
-Offer the presentation if they are ready
-Offer a "modified" presentation if that is possible (for example, if a young child wants to touch the bead chains but is not ready for the counting work with them, they could be shown how to dust them thus satisfying their need to handle them)
-Offer a different presentation that would interest that child
-If you are about to give a presentation to a different child, but can give the first one the presentation right after, assure the child that in a few minutes you will show her that work. Until then she can watch the presentation you are about to give or do some other activity for a few minutes or wait, perhaps in your chair. Since most presentations (with the exception of a few math and language ones) take just a minute or two, this would not be a long wait.
I don't understand why teachers just say, "You can't do that because you haven't been shown that." This was not in my training!
As far as dropping off children:
I let the parents in my school come to the door and the area just inside. We have a "greeting" area with coat hooks and a bench and shelves for slippers and parents stay there.
There was a child who was having a difficult time separating from his mother after about a month of school. It started after a babysitting incident with the grandmother, though no one could figure out what the incident was (the separation issue came on suddenly while the mother was out one night and the grandmother was sitting with the children. the grandmother did not know what precipitated the anxiety and the child could not verbalize more than the fear that he would be lost.). I let her stay with him and do work with him, though I would normally ask a parent to sit on the bench by the front door. It was a bit disruptive, but since this was not a "typical" separation issue (came on suddenly, was very intense, was not just about school) and she was so respectful of how quiet to be and how to make herself "small" so as not to be too obvious it was okay. After over a week with no progress at home or at school (he would freak out if she walked into the garage to throw something away for fear she was leaving) she decided to have him stay home for a month so that she could just "be" with him. I visited to keep in contact with him and in January he returned and had no separation issues. His mother drops him off at the door and he comes in himself.
I have only, for one year, worked in a school with a "drop off" from the car policy. I must say that in areas of limited parking I understand it but I don't like it. As an administrator I would prefer that if this has to be the policy because of lack of parking space, perhaps the first year students would be "exempt," that is, perhaps they could "park" and be escorted to their classes by their parents as they are the youngest and in most need of a secure separation.
As far as the playground issue with your child hurt, I think this is unacceptable. I would never tell a child that they can't cry if they aren't hurt. Children can be scared, too, from a fall. Also, how does she know he isn't feeling hurt. This is certainly not a Montessori policy.
Well, I hope that you find a different place for your child, one that is more loving. Please understand, though, that none of these things is a "Montessori" policy.