What is the ruling on paying a sum of money to Saudi citizen in return of having Saudi residence? It is worth noting that this transation is labelled as a "worker's visa" but I am not going to work as such only to facilitate having it?

Is it permissible to move a grave from its current location to another place, for example, from a garden in a home to a cemetery, knowing that the grave has been there for a long time, about fifty years?

It is not permissible to move the deceased from his grave, as this may result in breaking his bones and violating his sanctity. Such actions are not allowed. And Allah Knows Best.

Is it permissible for us to sever ties of kinship if our blood-relatives` gatherings/meetings involve acts of sin?

Observing kinship ties is obligatory, and paying your blood-relatives a visit causing their sinful acts to be hindered , then you should do so. However, if their sinful acts continue while you are at their gathering and they didn't respond positively, then observing kinship ties via telephone and the like will suffice in this case. And Allah Knows 

Do certain vaginal discharges and incontinence of urine nullify ablution, and should underwear be changed?

A person afflicted with constant impurity due to urinary incontinence and vaginal discharges is obliged to make ablution for every obligatory prayer when its time is due, and after removing Najaasah (impurity), and wearing a clean diaper. He/she is obliged to pray immediately even if the impurity is being released, and he/she is obliged to remake ablution, and the aforementioned for every obligatory prayer.