Is it permissible for me to shorten and combine prayers, including Friday prayer, in my home, given that the nearest mosque is 40 miles away and that Friday prayer is held in this mosque with no more than thirty men attending?

If you intend to reside in a country for four days or more, you are not permitted to avail yourself of the concessions of travel. Therefore, you must complete the four-rak'ah prayer, performing it at its prescribed time without combining prayers. If there are Muslims in the country with whom the Friday prayer can be established, then it is obligatory upon you to perform it. If this is not the case, you are not required to go to another country to attend it; rather, you must pray Dhuhr. However, if you do go and pray Friday prayer, it is valid according to many scholars.