What is the literal meaning of Sallallahu?
Would it be right if I say 'Allah's salah/salat', which means Allah's blessings, Mercy.
Salla , is derived from Sila that means : Connection , link .. etc.
That's why Salah (prayer) is very realted to mentioning and praising ,
"surely, I am Allah: There is no god but I: So worship Me , and establish regular prayer for celebrating My praise "
" establish prayer for My remembrance." http://tanzil.net/#trans/en.sahih/20:14
[Saheeh International translation]
Salla Allahu , means: may Allah give Salat (or Salawat) .
Salla is a past tense verb , Allahu : is the subject. (Literally : Allah did Salat.)
It's mentioned usually when saying : May Allah give Salat to his Prophet. And it means here : mercy and blessings , or means : praising the prophet among the angels.