Is permissible to buy/sell with non-Muslim?
Yes buying/selling for a Muslim with non-Muslim is permissible as regards what is lawful.
I had my menstrual period at the beginning of Ramadan for six days, then it ended and I became pure. After four days, I started noticing some blood again, which has lasted for two days now, but it is not as heavy as menstrual blood. Is this blood considered menstrual blood, and what is the ruling regarding my prayers, fasting, and reading the Quran during this period?
All praise is due to Allah, and peace and blessings be upon our Prophet Muhammad.
The minimum duration of menstruation is one day and one night, and its maximum is fifteen days. Any blood beyond this period is considered irregular bleeding (Istihada). Since the bleeding did not exceed fifteen days, it is considered menstrual blood within the regular cycle. Therefore, you should not pray or fast until the bleeding stops and the signs of purity appear. If the bleeding stops before fifteen days from when it first started, then all the blood you saw is considered menstrual blood, and you must make up the fasts, but not the prayers. If it exceeds fifteen days, then the first six days are menstrual blood, and the blood that follows is considered irregular bleeding. Your prayers and fasting are valid, and there is no issue with them. And Allah Knows Best."
*This answer was updated on [18/5/2023].
What should a person, who delayed making up missed fasts of last Ramadan due to the continuance of the same excuse, do?
It is permissible for one, whose excuse for not making up missed fasts of last Ramadhaan has continued, to delay fasting until the excuse ceases to exist, and he is considered neither sinful, nor obligated to pay a ransom. And Allah Knows Best.
Is it permissible to combine and shorten prayers at home before traveling?
It is impermissible to combine and shorten prayers at home before traveling because a person is called a traveler once he/she departs the borders of his/her country, and offering prayer that way was originally intended to exempt a traveler. And Allah Knows Best.