Should the two rak'ahs of "Tahiyyat al-Masjid" (greeting the mosque) be prayed upon entering the same mosque more than once in a single day? And is it obligatory to say the "Salam" with the Imam if the worshipper misses one or more rak'ahs, before completing what they missed?

If someone enters the mosque for Fajr prayer, for example, then returns to the same mosque for Dhuhr prayer, it is sunnah (definition) for him to pray تحية المسجد (greeting the mosque) a second time due to the long interval between the two prayers. The pre-prayer voluntary (ratibah) prayer is sufficient in place of تحية المسجد. If someone misses one rak'ah or more with the Imam, he should stand up to make up what he missed after the Imam's taslim (definition), saying "Allahu Akbar," and he should not say taslim with the Imam until he has completed his prayer.