Mechitza for how many women?

Igros Moshe (O.C. 05:12):When is mechitza needed? 1) Is a mechitza needed when praying in a place not normally used for prayer e.g.the house of mourning? Do the women need to go into a separate room or is it enough to be physically separated?. It would seem that the halacha is that women in a house of mourning need to go into a separate room. The reason is that a house of mourning is open to the public which according to halacha always requires separation between women and men and surely at the time of prayer as I have already explained in Igros Moshe (O.C.. 1:39) However if the women don’t agree to leave, this does not prevent praying since it is is not common. However in the house of a chasan there is no requirement for a mechitza since it is not open to the public but only to family members. Therefore it is sufficient for the men to pray in one corner 2)Is a mechitza needed if there is only a small number of women- one or two? In Igros Moshe (O.C.1:39) at the end I brought a proof from Kiddushin (52b) that there isn’t a need to have a mechitza for just a couple of women. So how many women don’t require a mechitza.e.g. in a house of mourning or in a yeshiva where they pray only Mncha during the week and Shabbos and it doesn’t have a mechitza? Is it permitted to allow a number of women to enter and sit at the end of the room? It has been true that in every generation that the normative practice to allow occasionally for a poor woman to enter the yeshiva to collect tzedaka or for a woman in mourning to say kadish, However the actual halacha needs to be researched and it depends on how many poor people there are. Nevertheless it appears that in yeshiva, that if they come every Shabbos and Mincha that there is no basis for leniency for prayer without a mechitza but it is permitted if this isn’t a fixed occurrence.  But this is true only when there is not more than two women. As you mentioned that according to halacha one woman can enter the yeshiva as can be seen in Shulchan Aruch (O.C. 282:3) that a woman can be counted as one of the seven.  3) Can a woman give a lesson in Shul or yeshiva when it is not time to pray such as Friday night when normally a lay person gives a lesson regarding the Torah reading and men and woman come? It appears that it is a great problem if men and women sit together but I don’t want to deal with that. The giving of a lesson by a woman is permitted but only if it happens occasionally. It is also required that everyone be seated during the lesson so it is more modest. It is also better to do it only in a private house and not yeshiva or shul.