What causes little brown spots on the shrub?
This is likely fungal leaf spots.
Symptoms generally appear in summer but will remain on the plant through winter and can still be appearing in spring.
Leaf blights also cause browning leaf patterns, they differ in that the spots will forms together and the entire leaf will turn brown and drop.
Control is generally with good care and sanitation.
Clean up any dropped leaves and discard of. This helps the spores from spreading.
Good care of the shrub with proper sunlight, air circulation, and fertilizer schedule will help manage these diseases.
Chemical treatment is generally not necessary, but a fungicide can be applied.
https://www.gardeningknowhow.com/ornamental/shrubs/mountain-laurel/mountain-laurel-growing.htm
Not doing good...leaves are falling off. How to grow it?
Look for identifying markings or color changes on the leaves.
These articles will help with care information and common disease issues with this tree.
https://www.gardeningknowhow.com/ornamental/shrubs/mountain-laurel/mountain-laurel-growing.htm
https://extension.psu.edu/pests/plant-diseases/all-fact-sheets/mountain-laurel-disease
How do you treat the seeds of the plant to grow the plant?
This link will help you with seed germination.
https://aggie-horticulture.tamu.edu/newsletters/hortupdate/2011/sep/grow-cb-tml.html
My mountain laurel shrubs have developed brown spots on the leaves. These appeared almost overnight after some recent heavy rains. No sign of insects or mold. Any suggestions? Thanks in advance for your help.
Various leaf spot fungi cause yellow, brown or black dead blotches on mountain laurel leaves. These blotches frequently run together, causing heavily infected leaves to turn yellow or brown and fall prematurely. Cool, moist weather encourages these diseases, especially when new leaves are developing. Shake out all fallen and diseased leaves from the center of each laurel shrub and destroy them. Remove all dead branches in the center of individual plants or hedges to allow better aeration. Mulching helps prevent the disease from splashing up from the ground and infecting plants. Spray at weekly to 10-day intervals with sulfur or copper fungicide, particularly in rainy weather. Dig up and discard seriously infected shrubs together with the root system and soil ball.
https://www.gardeningknowhow.com/ornamental/shrubs/mountain-laurel/mountain-laurel-growing.htm
Is in possible/practical to start Mountain Laurel plants from cuttings. I have a well developed, more that 50 year old plant that needs to be trimmed almost every year. What is the best type of wood for a cutting and what preparation leads to the best results?
You can propagate with cuttings and a soft cutting, on current green growth has the best chance of survival.
Take slightly green and pliable cuttings in the fall, just before dormancy.
Use a rooting hormone on the cuttings, either liquid or powder formula.
Fill pots with equal parts sand and perlite and have a clear cover or plastic bag to cover the pot.
The medium should be kept moist and at a constant temperature of 75 degrees with a germination mat.
It can take 4 to 6 months for the cuttings to root.
When is it best to plant mountain laurel?
Spring or fall planting.
https://www.gardeningknowhow.com/ornamental/shrubs/mountain-laurel/mountain-laurel-growing.htm
Our Homeowner's Association located about 30 mi South of Tucson, AZ maintains a common grounds cactus garden. It does contain a Texas Mountain Laurel, established plant for several years, about 3 ft tall, some nearby shade, no reflection from any nearby walls. What watering, fertilizing, and mulching care would experts recommend for it?
This article will give you some basic information on the care of these: https://www.gardeningknowhow.com/ornamental/shrubs/mountain-laurel/mountain-laurel-growing.htm