Who can write a get?

Tosafos in Gittin on 22b says that to write a get one need not be a "bar krisus", i.e. one who himself is fit to write a get (for example - a non jew who doesn't give a get because non-jews have no ishus). He proves this from the fact that the gemara only says a non-Jew cannot write a get because he doesn't have proper intention lishma. So, you see that otherwise a goy could write a get. Another proof of Tosafos is from milah. Just like by bris milah one need not be a "bar milah" to perform a milah, so too by get one need not be a "bar krisus" to write a get.
The Rambam in Hilchos Gerushin 3:25 seems to clearly imply otherwise, that one does need to be a bar krisus to write a get. The proofs of tosafos need to be answered by the Rambam.
Rashi also, in Gittin 9b (entitled: pesula) also implies like the Rambam when he says there is a drasha of "v'kasav v'nasan - that only a "bar nesina" can be a "bar kesiva" (meaning only one who can give a get can write one). Again, Tosafos proofs are questions on Rashi. We will present answers to these questions in another post. In the meantime, for anyone interested here are some maareh mekomos - Shiurei R' Shmuel on 10b in Gittin, Ginzei Hagrach siman 32, and Birchas Shemuel siman 16 in gittin.
The main issues we will address are the following. First the relationship between writing a get lishma and the requirement of being a bar krisus. Perhaps there is a din that a non-bar-krisus is incapable halachically of writing a get lishma. It's not that he doesn't have the proper intention, rather he doesn't have the halachic ability to create such a challos.
Another relevant issue is the comparison between milah and get. Milah is an actual maaseh mitzvah, whereas get would at first glance be merely a hechsher for the real maaseh of giving the get. What is the comparison of tosafos. Finally, one last point. Why does Tosafos not mention another gemara in gittin which talks about whether one who writes the tefillin must be one who also wears tefillin. That is a din that seems highly relevant to this issue of writing a get, yet it is completely ignored by tosafos. We will tie all these issues together iy"h.