In the Dallas - Ft. Worth area. How far from the house foundation should holly bushes be planted?
This certainly will depend on the variety that you are planting.
I general guideline is small shrub 2 feet from foundation, 3 feet for medium shrubs, 4-5 feet for larger shrubs.
Use the mature size of the Holly that you are growing to determine it's size.
What causes the tips if the leaves to turn brown and then fall off?
Leaf tips often turn brown when the plant's roots are having trouble absorbing water or are exposed to excessive fertilizer or salt. This article will help: https://www.gardeningknowhow.com/plant-problems/environmental/what-causes-brown-edges-on-leaves-of-plant.htm
Transplanted in spring. Fabric mat and stones added in the area around the bush. It was doing great and suddenly the leaves are all turning yellow. It looks like it is dying. The soil is moist and the new location is 2 feet from the old.
You could have a few issues going on here. If it has been hot and dry this new shrub may be needing more water.
Newly planted this spring it may not have the root structure to hold up to warm summer temperatures yet.
Yellowing leaves can indicate watering issues. Either to much or to little.
I also see some insect webbing in the image. This could be Spider Mites.
I would trim away the dead material and dispose of. Increase watering if it is dry.
Treat the Holly with Neem Oil, as use weekly for the remainder of the growing season.
Here are some links for you.
https://www.gardeningknowhow.com/ornamental/shrubs/holly/growing-holly-bushes.htm
https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm
Can you take a branch on a holly tree and put it in the ground to make it take root?
Yes, you can take cuttings from holly and encourage them to grow roots. However there is a proper procedure to follow; please see the following articles.
https://content.ces.ncsu.edu/plant-propagation-by-stem-cuttings-instructions-for-the-home-gardener
https://www.gardeningknowhow.com/ornamental/shrubs/holly/holly-cuttings.htm
https://www.gardeningknowhow.com/ornamental/trees/tgen/how-to-root-cuttings-from-various-shrubs-bushes-and-trees.htm
Recently purchased this house with a large holly bush. Noticed that bush has leaves and berries on the outside only, with no growth on the inside. Does not look as though the bush was ever pruned. I do not know what type it is, and do not want to kill it by incorrectly trimming. Do I need to cut some holes in the bush to allow light to access the inner bush? Could use some advice. Thank you
You are probably correct that the interior of the bush cannot access enough light. Pruning some of the branches back will help with this. Here are some articles that will guide you:
https://pubs.ext.vt.edu/430/430-459/430-459.html
This article provides a lot more detail that applies to hollies as well as other shrubs:
http://extension.uga.edu/publications/detail.html?number=B949
I have 3 holly trees at the end of our garden, which are about 15 foot tall. One of them has something growing at the top of it and has prolific white flowers. Do you know what this is?
This could be a parasitic plant, a plant that derives its energy by feeding on other plants. Dodder is a yellow-stemmed twining parasitic plant that has white flowers. If it's dodder, you will be able to see its yellow vine-like stems.
Or, it could be an ordinary vine which has climbed up the holly. In this case you would see the stem of the vine climbing up the holly from the ground. Hopefully it's not poison ivy, which has white flowers!
My two holly trees do not have dense growth. Would pruning help? Both trees have good leaf and berry growth but are not showing dense growth. How can I improve for dense growth?
Yes, pruning will help shape your plants.
I would also check soil conditions and light since the shrubs are close to the house.
Here are some links for you.
https://www.gardeningknowhow.com/ornamental/shrubs/holly/trimming-holly-bushes-how-to-prune-holly-bushes.htm
https://www.gardeningknowhow.com/ornamental/shrubs/holly/growing-holly-bushes.htm