How tall do I let Rosemary grow, and when do I start cutting some?
Once it is 6" tall, you can start to trim it for use. It is best to trim it at about 6" regardless, to help encourage branching for a fuller plant.
My rosemary bush is very large. I am in the Northern Neck, VA and the plant has grown beautifully, but in the last year the bottom area under the green has become brown. A lot of coarse and hard, brown stems. I have never trimmed or pruned it. Can I cut it all back (the brown areas) and then it will come back, cut it all back (and it will all come back as it says in your section about them and do it in stages), or leave it alone? Any help will be appreciated as I have never seen one this big before.
You can do what is called rejuvenation pruning. Rosemary responds will to that when it has aged and gotten woody. This article has a section on how to perform this kind of pruning (about half way down):
http://pubs.ext.vt.edu/430/430-459/430-459.html
My rosemary bush is emitting very little fragrance, and the leaves are dry to the touch and show signs of yellowing.
It sounds like the plant may be overwatered and may be dying because of it. Cut back the amount of water given the plant. This article should help you with rosemary care: https://www.gardeningknowhow.com/edible/herbs/rosemary/growing-rosemary-plants-rosemary-plant-care.htm
I have some very healthy rosemary plants growing in full sun. Now there are dozens of spider pods all over them. How do I get rid of them? Will they kill the plants and other plants?
Spiders don't harm plants and can be beneficial in keeping unwanted pests from getting at the plant. If there seems to be very many of them, the best organic method would be to simply use your water hose to spray down the plants and knock the spiders and their pods off. It won't get rid of them all, but will reduce how many there are. To be honest, if they do seem to be hanging around, they are probably well fed off pests from the plant and may be keeping your plant from those pests.
If, however, you are referring to spider mites, then you can treat with neem oil, which is safe for beneficial insects (and spiders) but will kill those that are harmful. Here is more info: https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm
I am trying to transplant rosemary. You say to put it in a 'potting medium'. What is that?
Potting medium is just a fancy way of saying soil or the any of the many other things you grow plants in. Not all potting mediums are soil (dirt), some are part soil and some can be soliless.
In a word, soil. Use a good gardening mix - don't be tempted to buy the $1 bags of muck that some retailers call gardening mix. You need one that drains well. I don't know if we are allowed to use brand names here but an example would be Miracle Grow Planting Mix sold at almost every garden center.
I have rosemary plants in pots; they are turning brown. I water every evening and they get the afternoon sun. It has been very hot in Arizona, the temps are over 100 degrees. What is going wrong?
The following articles also should be of some help to you: https://www.gardeningknowhow.com/houseplants/hpgen/how-to-water-a-plant.htm
https://www.gardeningknowhow.com/edible/herbs/rosemary/watering-rosemary.htm
What size are your pots? If these are in small pots, they will dry out in a matter of a few hours. AZ is like Texas - just blamed hot and rainless. If in small pots, I would transplant into larger pots and try to water twice a day until they are well established. It is probably just stressed since rosemary is tough.
What is the best way to save Rosemary during the winter months when freezing it?
Lay out flat and in one layer on a metal cookie sheet in the freezer. Once it is frozen, place in a freezer bag and remove as much air as possible. Place it back in the freezer and use as needed. The rosemary will turn black. This is normal and it will still taste fine.