1. Is refusing marriage to care for a sick mother an act of righteousness or a sin? And is the sin great? 2. Is delaying prayer due to the long distance to the university a sin?

If refusing marriage leads you to commit unlawful acts, then it is forbidden. Marriage becomes obligatory for anyone who fears committing zina (unlawful sexual intercourse) and is capable of marrying, in order to protect themselves. If you feel secure from fitna (temptation/tribulation), then there is no harm in delaying marriage, but expediting it is preferable, and repeated rejections may lead to lost opportunities for marriage. Honoring and caring for your mother are among the greatest obligations. Marriage can be combined with fulfilling this by informing the suitor or hiring someone to serve your mother, while maintaining your continuous honoring and care. If this is not possible, then you must serve your mother, and you will receive a great reward. Delaying prayer beyond its prescribed time until it expires is not permissible. Going to university or not hearing the adhan (definition) (call to prayer) are not valid excuses. Rather, you must know the prayer times and pray wherever the time for prayer overtakes you.