Shingles is caused by the same virus that causes chicken pox. After you've had chicken pox initially, the virus will lie dormant in the nerves in spinal cord and brain.
At any time, the virus can be reactivated, causing a painful rash (shingles) on one side of the body. So, to answer your first question, even after the first outbreak shingles can occur on the opposite side of the body, as it really depends on where the virus is.
Shingles in the head or face is always concerning, as the virus can cause a rash near your eye. If the virus gets into the eye and is not treated properly, this can lead to permanent eye damage. If you have the rash near your eye, you should see an opthalmologist as soon as possible.
Your 2nd question is about the head and neck being along the same nerve as under the left arm. The left side of your head and the neck are along the Cervical 2/3 nerves, while the underside of the left arm is along Cervical 5/6 or Thoracic 1, depending on where your rash is located. So, no, the head/neck is not included in the left arm nerve.
Since you have had shingles twice, you should consider having the shingles vaccine once your rash goes away. This can help reduce the risk of shingles in adults age 60 and older who've had chickenpox. The shingles vaccine cannot guarantee you won't get shingles ever again. But the vaccine may reduce the severity of the rash, while reducing the risk of postherpetic neuralgia, which is a painful condition that happens in the nerve once the shingles rash has disappeared.