Is it permissible to travel to European countries for work to improve one's financial situation, and is it permissible to dream of a comfortable financial future, building a family, and buying a home, while Muslims are suffering in Palestine, Iraq, and Chechnya?

A Muslim resides where they are able to observe the rites of their religion and are safe from tribulation, whether the country is Islamic or non-Islamic. So, if you are confident in your ability to practice the rites of your religion and your salvation from tribulations, then there is no impediment to your travel to non-Muslim countries; otherwise, there is. A Muslim must care about the affairs of Muslims, and there is no harm in enjoying permissible blessings, as long as it does not reach the point of extravagance or neglecting obligations.