Okay, doggie is doggie.  Easy, the bottom is on knees and hands (or elbows) and gets it from behind.

With shemales, is Missionary like front-to-front boy/girl, but without the ability to embrace because the top on his/her knees?  If not, what is this called?

What is it when the bottom lies flat on his or her (shemale) stomach and the top enters her from behind while covering her from head to toe?  This seems more equivalent to hetero missionary than the face-to-face above, although I don't remember reading about gay or TS evangelists.

Who's the expert here?

Since the term describes the position (and not the individuals), I wouldn't think the names for the positions would be any different.

Of course the names are the same.  But what is the name when both are face down?

The Kama Sutra refers to that position as Coitus From The Back (under Perfumed Garden positions). Geez, you might have expected a little more imagination with that name. How about Cobra On A Limb? Cosmopolitan magazine calls it The Carnal Clench, rating it a 3 (out of 10) degree of difficulty, and a 9 on their heat meter. Amorous lumberjacks refer to it as the Laminated Plywood position.

Since the both-face-down position seems to have gone begging for a colorful name (Missionary, cowgirl, doggie, etc., all conjure up a visual image) we should try to think of some physical act that resembles it.  Or, alternatively, we could name it for someone.  Staff and Wantats come to mind.  Ideas?

I believe "spreadeagle" is what you are describing ; from a couple of sources; and edited a bit.

the position in which a person has arms outstretched and legs apart, figuratively resembling an eagle with wings spread. It can refer to the sex position in which one partner is supine in a spreadeagle.

One partner lies face down with the other on top ... bottom spreads their legs ... while lifting their bottom off the bed slightly (with a pillow, etc.), to achieve deeper penetration. The top supports his weight on his arms or lays with his full weight on his partner.

drunk?
Passed out?