"that she bears": to exclude (from yibum) a woman who cannot bear.
(The yavam) "shall be invested in the name of his dead brother": for inheritance (i.e., he receives his dead brother's share as well as his own.) It is written here "in the name of his brother," and, elsewhere (Bereshith 48:6) "in the name of their brothers (Ephraim and Menasheh) shall they be called in (taking) their inheritance." Just as there, the reference is to taking inheritance, so, here.
"his dead brother": Because it is stated elsewhere that the wife of one undergoes yibum and not the wife of two, whence do I derive that if the first brother died, the second performs yibum; if the second died, the third performs yibum? From (the repetition of) "dead" (verse 5) - "dead" (here).