Is it necessary to breastfeed from both sides in one feeding?

No. Many moms have lots of milk, and many babies are satisfied with just one breast. The general recommendation is that if you feed only one breast, then start the next feed on the un-nursed side. I recommend to pump the side he did not nurse. This builds a supply for dad to be able to feed the child. Pumping also prevents being lopsided, which can be uncomfortable.
No. But it is more comfortable for most women to relieve breast engorgement on both sides at each feeding. Some feed one side and pump the other if they have more milk than the baby can use.
No. The first milk in the breast, the "foremilk" is low in calories and is a thirst-quencher. As the feeding goes on, the fat content is higher, the "hindmilk." the baby benefits from getting both the foremilk and hindmilk and should stay on one breast until they take themselves off. The second breast can be offered, but isn't necessary. Artificial time limits on feeding are, well, artificial.
No. It is not necessary, but you might get engorged on the unfed side, so using both breasts at each feeding is preferred.
No. It is not "necessary"- many mom's try to nurse from both breasts each feeding to avoid feeling overfull or engorged on one side. Also, babies can start to "prefer" one breast over the other. So, in general, let the baby nurse for 7-15 min on the first breast, then switch. If the baby does not take the second breast, you can express some milk, and be sure to start on that breast for the next feedin.
Yes. Ideally at the beginning you should try to record the time and duration of each breastfeeding, and to determine whether the amount of urine and stool is adequate for your baby's age also, it is important to see that the baby is growing.
No. Not absolutely and certainly not mandatory for the baby, especially if mom's supply is really strong. Most people will recommend some feeding off the other side, however, if only to 'take the edge off' of the fullness you might experience waiting until the next round. In short, if the baby is gaining strong weight and mom isnt uncomfortable, then it really doesn't matter.