In the middle of the night or early morning, my grapevine leaves are being eaten by something, not in the sense that there are little holes; they are cleanly cut and the stem of each leaf is left. The vine currently stands 3. 5 feet off the ground and is on a trellis. I can't imagine that a rabbit could get that high to reach the top leaves. I live in Mesa, AZ (metro Phoenix area), but with plenty of open desert across street and behind my yard. I have block fencing, so the only thing that could get in would be something small enough to get under my gate or fly over it. Whatever was eating the leaves was originally only eating the ones closest to ground, but this morning I came out and they were all gone! Something is also devouring my Hearts and Flowers (Aptenia cordifolia). They aren't as cleanly cut, but are being chewed to nubs.
Try using neem oil. It is organic and very effective against many insect pests. Here is more information: https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm
What kind of soil do you need for grapes and where do you get it?
Grapes prefer a rich soil with lots of nutrients. Normally, you would plant them in the ground in your garden, so you don't need to get soil from somewhere but you may need to amend you soil to grow good grapes. You can grow grape in containers as well and Miracle Gro soil is great for growing them in a container. You will need to provide them with enough water, since they cannot grow deep roots to find water, but as long as you can provide the water, they will be fine. Typically, in a container, they will need water every day during the summer and need some protection from the cold in the winter. I would recommend using a slow release fertilizer, like Osmocote, on it during the summer to make sure it gets enough nutrients.
I planted a Lakemont seedless grapevine and wanted to know if I should be providing any feeding or soil conditioner, similar to how I provide soil acifier to blueberries. Also, do blackberries require or need feeding?
I give my tomato plants sodium phosphate. Is it ok to provide this feeding to my other vegetable plants like cukes, radishes, lettuce and carrots? Are there other fruit bearing or flowers that can benefit from sodium phosphate?
They don't need acidifiers, but for both plants, fertilizing once a year will help them grow better. Any plant that flowers or fruits benefits from the addition of phosphorus. Just be careful for any plant, including the tomatoes, that you do not add too much.
I recently moved into a new (old) house. In cutting out a thick bunch of Virginia creeper, I realized that I had also cut off a very old grapevine. The 'trunk' of this grape is about two inches in diameter. I see now that it has some new growth coming on it. Will this grape be okay and possibly fruit? And will it grow enough to fruit this year, or will it be next year?
The grapevine should be fine. In fact, it too can benefit from an occasional pruning. Here is an article that you may find helpful: https://www.gardeningknowhow.com/edible/fruits/grapes/prune-grape-vine.htm
Is it okay to prune grapevine during mid spring/early summer, or will it damage the vine?
You can. You may affect the fruiting of the plant, but the plant itself will be fine.
Is it ok to prune a grapevine in late spring (northern Illinois) or should pruning only be done in the winter? When is the proper time to propagate a grapevine?
These articles will help: https://www.gardeningknowhow.com/edible/fruits/grapes/prune-grape-vine.htm
https://www.gardeningknowhow.com/edible/fruits/grapes/growing-grapevines.htm
My Grapevine leaves have brown spots on them. How can this be corrected? What kind of food can I give the vines?
This could be a number of things--too little or too much water, over fertilizing, leaf scorch, etc. I would recommend using a slow release fertilizer, like Osmocote, on it during the summer to make sure it gets enough nutrients. This article has more information: https://www.gardeningknowhow.com/plant-problems/environmental/what-causes-brown-edges-on-leaves-of-plant.htm