I had some pine trees in my yard, pruned/trimmed, and iInotice they are dripping sap like crazy. Is this normal?
Yes, this is normal. While Sugar Maples are the most famous tree for running sap this time of year, almost all trees have increased sap production at this time of year. If the trees are trimmed ot otherwise cut, the sap will ooze some out of the wounds. It does not harm the tree though to lose this sap.
What do pine tree seeds look like?
They are small and brown to dark brown in color—found in unopened pine cones. If the cone has already opened, chances are the seeds have dropped out.
My pine trees have a white foamy, watery residue. Is this bad for the tree?
Sounds like a spittle bug problem. Here is an article that you may find helpful: https://www.gardeningknowhow.com/plant-problems/pests/insects/spittlebug-control.htm
I wanted to try growing a pine tree from a cone that I gathered, but is it too early in the year to do this? Would it be possible to start a tree from purchased seeds?
It would be possible to grow a tree from seeds that you bought.
When and how to start the seeds though would depend on which variety you are growing. If you can let us know that, we can get you directions on how to do it.
How do you remove pine sap from hands and bottoms of leather shoes with rubber grooved shoe soles?
This article should help: https://www.gardeningknowhow.com/ornamental/trees/tgen/how-to-remove-tree-sap.htm
My mother-in-law lives in Hemet, CA and has many pine trees, two of which are mature and completely dead. Two other mature pines are partially dead. Brown needles on the top and most branches but with one to three branches which are green and look healthy. Can they be saved?
Do you know the varieties and, other than brown needles, are there any other signs of problems, such as bugs or anything like that? This information will help us diagnose the trees.
It sounds like the trees may be succumbing to a blight that affects that particular kind of pine tree. I could be wrong because this blight normally only affects part of the tree, but any bight, if it is severe, can kill a plant. This article has more information on it:
I have large pine trees and want to plant Hosta or some border bushes and plants, maybe perennial flowers in the pine straw under them.
Pine trees tend to have acidic soil, but most plants can handle the acidity. The real problem will be the fact that the tree will suck up all the water. You will need to make sure the plants under the tree get extra water to offset this.