Perform the number of prayers that you are certain you have missed with the intention of obligatory qaḍā and if you want to perform more than that, perform them with the intention of precautionary qaḍā.
You should perform the sign prayer for each earthquake that is felt, but if it repeats during the prayer then that prayer will suffice. If repeating the Sign prayer causes considerable hardship for you, then you can perform it as much as is convenient for you.
Attending their Friday Prayer with the intention of creating a great unity among Muslims is good and suffices in lieu of noon prayer on Friday. Furthermore, under such conditions, there is no issue with prostrating on carpet.
It is permissible.
According to some traditions, this phrase has been recited as a part of the call to prayer since the age of the Infallible Imams (‘a) but it was not widely recited in that era. Later on it became the motto of the Shiʻa school (for more information, refer to the valuable book of “al-Mustamsak”, chapter on adhān and iqāmah).
They can perform the prayers simultaneously.