Tahiyaat al Masjid

As salamu aleykum,

If one makes Wudhu and enters a Masjid 10 minutes before the Azaan’s of each prescribed Salaat i.e. Fajr, Zuhr, Asr, Magrib, Isha.

At which Salaats one can pray the Tahiyaat al Masjid salaat i.e. 10 minutes before it?

Also, does this Tahiyaat al Masjid also counts as Wudhu-salaat? Or does one has to pray that seperate?

Was salaam