Parshas Noach:The Status of A Ger Toshav

This weeks chaburah was on understanding the status of a ger toshav.
Note: Due to the nature of this topic I am being m'katzeir and providing mareh m'komos. v'hameivin yavin. (If you can convince me that I am being overly sensitive I will provide greater detail).

The gemara in Avodah Zara (65b) brings a machlokes in understanding what makes a ben noach into a ger toshav. The Rambam (Hil Avodas Kochavim perek 10 and Hil Issurei Biah 14:7) paskens like the chachamim that a ger toshav is a ben noach who accepts on himself in from of a beis din that he will keep the 7 mitzvos b'nei noach. The Rambam also adds (Issurei Biah and in Melachim Perek 8) that one who accepts on himself to be a ger toshav is from the chasidei umos ha'olam and gets olam haba. However, if a ben noach keeps the 7 mitzvos on his own then he does not get the special status of a ger toshav.
The Ritva in Makkos (9B) also writes something similar ayin sham. A ger toshav is a metzuvah v'oseh and a ben noach is aino metzuvah v'oseh.

In terms of what special laws apply to a ger toshav, ayin the Chazon Ish Baba Kama Siman 10:16.

The Brisker Rav (mechtavim in Chiddushei HaGriz, last letter) explains that the status of ger toshav was created after mattan torah and he bases this on the gemara Baba Kama 38a and the Ritva mentioned above.
The lomdus boils down to whether it is a real geirus or just a kabbalah in beis din. The Brisker Rav feels it is just a kabbalah to keep teh 7 mitzvos and it brings with it certain dinim. The Mishans Ya'avetz (Y.D. Siman 3) brings many ra,ayos to show it is a type of geirus and the cheftzah of the ben noach is affected. Rav Asher Weiss in Minchas Asher brings many of the ra'ayos of the Mishnas Ya'avetz (but he doesn't quote the Mishans Ya'avetz so presumably they are his own ra'ayos as well) and then shows how they are not ra'ayos.

The nafka mina would be could a ger toshav be chozer and are his children geiri toshav. The Brisker Rav writes explicitly that a ger toshav can be chozer by not keeping the mitzvos since it is not a real geirus and jsut a kabbalah.
If it is a real geirus then the children should also be geiri toshav

The Chazon Ish writes a ger toshav can be chozer but he also says the small children of a ger toshav are geiri toshav. This seems to be a bit of a stirah. (Although tzarich iyun why davka the small children and not all children)