What is the ruling on the fast of one who was afflicted with a severe cold in Ramadan and did not pray for two days due to his inability to find anything with which to perform tayammum in Western countries? And is it obligatory for him to re-fast that day, pray therein, and strive in performing qiyam al-layl?

You must repent from being negligent in abandoning prayer, as a cold is not an excuse for abandoning it or a barrier to ablution. You can perform ablution with warm water. Prayer is not forsaken as long as a person is sane. You must immediately make up for missed prayers in their proper order. Your fasting is valid and does not need to be repeated. Be diligent in learning what makes your worship valid.