Steve ... The plant looks OK .. but get it out of that pot .. the box you bought it in is not meant to be a permenant container .. and it's been in their way to long. Check the the roots to make sure they are not growing in a circle .. if so pry them apart a bit before replanting. Also ... get rid of that nursery stake ... it will seriously wound the tree ... if you must restake use two stakes secured loosely to allow the tree room to move and grow without injury. Give the plant a good washing down once in a while .. that will help the dust problem. The temps you mention are no problem for this plant but they do get a bit weather beaten in winter and growth will slow or stop at this time. The plant can take a considerable amount of sun and do well in moderate to moderate heavy shade. At my home they do great growing as foundation plants on the north side of my two story home. Avoid reflected heat from patios .. walls or rock mulch. Use organic mulches around this plant. The best bet with water is to pry into the soil .. look for moist but not soggy conditions and a clean earthy smelling soil not rotten egg smell. The plant will do better in the ground but can be grown in large pots with drainage... about three times as wide as what you have now. Flush pots out once in a while to reduce salt build up. The main problem with this plant in deserts is iron deficiency ( yellow leaves with green viens 0 .. salt build up ( leaves with yellow then brown tips and edges ). They need decent drainage so watch water carefully if planted in the ground .. pry into the soil. All in all a tough plant. Try giving the plant a rest from pruning for a while. End of winter pruning is best .. light pruning anytime... be careful in summer ..pruning can expose shade leaves to sun and cause leaf burn .. ugly but not fatal. Good luck. Good Day ...

Waxleaf Privets do exceptionally well in a pot, if they are watered frequently---they do not need to be watered as much as say, a rosemary. They can be root bound and survive. They will grow in sun or shade. They can be easily shaped into very decorative spheres, boxes, poodles, small trees, etc. You will not have that many birds feeding on it's seeds (distributing them) if you keep it on a porch (and I have not seen any growing in the wild but then again, there is usually little ground water around here).

with a new planting.. i would not prune for at least two seasons ... the first to let the roots settle in and get established.... the second to grow free .. to work towards the goal i wanted to accomplish not know the size you have now.. nor your goal.. nor a pic.. its hard to give any real advice ... pruning is not really requisite.. for the hell of it ... lol ... what is your goal?? ken ps: as one examply .... usually privet is sheared into a box-like form ... but one might prune it into a topiary design ... so a good start .. would be looking up the terms.. and using the one that more closely aligns with your future goal ... a good start at the link.. flip to the ALL side.. and look at the first link ... after reviewing something like that.. you can narrow down your goal.. then we can offer much more precise info ... https://www.google.com/search?q=privet+pruning+vs+topiary&source=lnms&tbm=isch&sa=X&ved=0ahUKEwimqYnjhLHKAhWBKCYKHdnaD4cQ_AUICCgC&biw=967&bih=745&dpr=0.9

About a month ago I cleared away all the dead leaves from the under the plants, and applied some 15-15-15 fertilizer. I haven't noticed any improvement, ==>>> think in plant time..not your instant gratification expectations ... i would not expect and noticeable change.. until next springs growth spurt.. in my MI ... perhaps they grow year around in CA ... but even so ... there has to be major growth seasons ... ALL evergreen trees are near bare inside.. and shed leaves in a cyclical nature .... so that part doesnt bother me ... you might also look into REJUVENATION PRUNING OF FLOWERING SHRUBS .... if you ever wish to knock this thing down a bit ... i would not water a shrub of this size and age.. nor fert them.. ever ... they would be on their own .... ken https://www.google.com/search?q=REJUVENATION+PRUNING+OF+FLOWERING+SHRUBS&ie=utf-8&oe=utf-8#q=REJUVENATION+PRUNING+OF++SHRUBS