Is it permissible to swear by (Allah "The Living")?

Yes, it is permissible because "The Living" is one of Allah`s Attributes.

A person prays in a certain spot within the rows of the mosque, and gets angry if someone else prayed at his spot. What is the ruling on this behavior?

All Perfect Praise be to Allah The Lord of The Worlds and may His Peace and blessings be upon our Prophet Muhammad and upon all of his family and companions                                                                                                                                                                                                                              Prophet Mohammad (PBUH) make it prohibited for a Muslim from having/taking a certain spot in the mosque when performing prayers if they arrived and find it occupied, furthermore; it is the religious duty on others (praying people) to offer a piece of advice to alert the ones who don't know, that whoever reaches a spot first at the mosque having a priority/privilege upon others in that spot. And Allah Knows Best.

I`m a cashier at a branch of the Civil Service Consumer Corporation. Sometimes, customers pay more than the due amount. Do I have the right to take that extra money knowing that I cover shortages from my own salary?

Is it permissible to add the nutmeg to one`s food?

Using a little bit of the nutmeg for seasoning is permissible, but using a great deal of it is impermissible since it could lead to intoxication, and Islam has forbidden all intoxicants and stupefacients. And Allah Knows Best.