Once you believe in in Allah, then anything Allah says is proof. All these questions branch out from the question of is Islam true or not. After we have proven Islam Is the truth (which has been proven) then anything that Allah says is the truth. We don't need any empirical evidence for existence of hell or heaven. Allah's word is the proof. Also same for al-lauh al mahfuz, Allahs throne, angels... Etc.
This Book, there is no doubt in it, is a guide to those who guard (against evil). Those who believe in the unseen and keep up prayer and spend out of what We have given them. [2:2-3]