Bermuda does grow in zone 7b Texas, but at this time of year most turf is dormant. You will need a good amount of sun for bermuda, I'm not familiar with the teff variety. If you want a green lawn now, you can sow annual rye, it is cool season grass that will go dormant when it warms up in the spring.

I have a lot of shade and in some areas, bare spots. I try to grow groundcover that tolerates deep shade in those areas or situate shade gardens with other tolerant plants. Depending on your preferences, a patio area under trees is nice when it's warm out.

Bermuda will probably grow on the moon! It is very easy to grow (even from seed) but won't grow in full shade. It will run quite rapidly, so if you have beds that you don't want to weed, you may want to think of something else. I have Bermuda myself, but have heard great things about Turfallo. Not sure if I spelled that right.