Travelers have the right to perform their prayers in al-Masjid al-Harām and al-Masjid al-Nabawi and also all of Mecca and Medina complete or shortened and complete prayer is better and there is no difference between old and new parts of Mecca and Medina.
1- It is not permitted. 2- It is like the previous issue. 3- Yes, you can ask all religious lawful matters from Allah.
This person can perform qunūt after rukū‘ and then go for sajdah without rukū‘ and continue the prayer.
This act is makrÙh (abominable) unless this is the only way of having presence of the heart (full concentration).