Question
I live in Central Florida and I have a large 20-30 year old golden raintree in my front yard that is displaying symptoms of illness. I've seen neighbors trees (this tree is very popular in my neighborhood) and none of their trees look like this. The symptoms include:
1) Prematurely yellowing leaves
2) smaller branches breaking off for no apparent reason
3) thinning crown
4) seed pods are drained of color (pale pink/white instead of bright red)
Upon inspection of the broken branches (mostly 1cm diameter or smaller), I've noticed what appear to be small bore holes inside the branch. I also recall noticing many blue and red beetles on the tree at the beginning of the summer.
Basically I've come to the conclusion that I have some sort of beetle larvae infestation, but I wanted a second opinion. Is it possible that the above listed symptoms could be the result of old age?

If it is probably an infestation...
Is there anything that can be done for the tree besides using the pesticide imidacloprid? I suspect that this infestation has been ongoing for years, but I just moved into this house this year so I have no knowledge of the tree's prior history. What is the likelihood that the pesticide would work? In other words, would it be worth introducing the pesticide into my yard (I am worried about the bees, birds, and my kids)? If the tree is likely to survive, I might consider the risk. Also, do tree injection kits work? Is there an advantage to using an injection kit instead of a spray?

Thank you for taking the time to read and answer my questions! I have been very depressed about my tree and I am looking for some way to save it!

Answer
There are several things going on with your tree. First the blue and red insect is a Golden raintree bug. And the twig problem is the Black twig borer.

First the twig borer. The black twig borer, Xylosandrus compactus, is one of the few ambrosia beetles that will attack healthy trees. However, a couple years of drought followed by periods of heavy rainfall year stresses many tree and plant species making them more susceptible to insect damage and disease. This beetle only damages branches that are approximately pencil size in diameter. These small branches die above the point of entrance with the leaves turning brown, creating a flagging effect of numerous dead branches scattered throughout the outer canopy of the tree. These dead twigs with their brown leaves are what bring attention to the infested trees.

Female beetles bore into small branches or twigs of woody plants, excavate tunnels in the wood or pith and produce a brood. Damage occurs when the beetle introduces ambrosia fungi on which the larvae feed. The beetles emerge in late February, attack twigs in March and brood production begins in April. Highest population levels occur from June to September. Adults spend the winter in damaged twigs and branches. So it抯 important to pickup and dispose of the small branches as they fall.

Where practical, the best control is to prune tree limbs 3-4 inches below the infested area, then remove and destroy the limbs. Proper mulching, avoiding over fertilization and irrigating during dry weather should improve tree health, allowing trees to better withstand attacks. Chemical controls are usually not practical or effective.

The best method is remove the dead twigs and fallen ones and destroy them and fertilize the tree with 10-10-10 fertilizer at the rate of 1 lb per inch of trunk diameter scattered around the tree and watered in good. Apply just before a rain storm and you will not need to water. Fertilize now and again in the Spring.

The Golden raintree bug.
Golden rain tree bugs (Jadera species), also referred to as Jadera bugs, soapberry bugs and red shouldered bugs, are called nymphs in their early life stage. As nymphs, golden rain tree pests display a bright red coloring with brown or black legs. In their mature, adult form, these pests are flatter and display a brown to red body hue with an abdomen with spots in dark red; the bug grows to 1/2 inch in length and 1/3 inch in width, according to the University of Florida IFAS Extension.

Damage from the golden rain tree bug is generally insignificant. The bug will eat the leaves, stems and seeds of the golden rain tree, but usually without causing widespread destruction. In large numbers they can weaken the tree allowing other insect like the borer to attack. These do feed on the tree so I would recommend the use of an insecticide called Bayer Advanced Tree and Shrub Insect control. This is applied to the soil around the tree and the roots will transport the insecticide to the twigs, fruit and leaves. And when the insect feeds on the tree they will be killed. It will not harm bes.birds or the kids since it is not a spray and is very safe. Injection of these type insecticides can damage the tree and allow decay fungi to enter the wound.  Here is the web link to the Bayer product--check with your local nursery for this product. I would wait until next spring to apply since the trees will soon shut down for the winter and the movement of the insecticide to the leaves will stop until next spring. It is a formulation of imidacloprid.This product will last the whole season.
http://www.bayeradvanced.com/tree-shrub-care/products/12-month-tree-shrub-insect