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Camphor trees are prone to chlorosis (yellowing) from nutrient deficiencies and are stubborn for greening up, it takes a couple or three applications of fertilizer a year, and sometimes a couple of years to see good results. They can also be affected by inadequate watering and low organic matter content so that available nutrients are not taken up and translocated throughout the foliar crown, Drip systems are often inadequate and you need to deep water by flooding a couple of times a month. Camphor are native to southern China where there are summer rains. You live in an area with hot dry summer and fall so good water managment is essential, as well as mulching to help retain soil moisture.

An all purpose complete organic fertilizer application in spring and fall is best for sustained slow release fertility.

https://www.gardeningknowhow.com/ornamental/trees/camphor-tree/camphor-tree-growing.htm

Cutting them, manually, would be a good step to start with. Keep any regrowth trimmed up until you plan to start leveling. If any are vigorous enough to stay alive through the constant trimming then you can hit those with boiling water. If you are not able to get boiling water out there then it will likely die from a thick covering when you level it. Still, should any remain, you may turn to things like vinegar or chemical herbicides.

Here are some articles that will help:

https://www.gardeningknowhow.com/garden-how-to/info/clearing-and-grubbing.htm

https://www.gardeningknowhow.com/ornamental/trees/tgen/weed-trees.htm

https://www.gardeningknowhow.com/garden-how-to/design/professional/when-to-call-tree-cutting-professionals.htm

https://www.gardeningknowhow.com/plant-problems/weeds/boiling-water-and-plants.htm

https://www.gardeningknowhow.com/plant-problems/weeds/post-emergent-herbicides.htm

There are several possibilities. Likely, either, the seedlings are sprouting (making a smell when cut), or the tree is leaking sap to the lawn below. Either way, there is likely no harm being done.

https://www.gardeningknowhow.com/ornamental/trees/camphor-tree/camphor-tree-growing.htm

It is possible that it could cause a slight slow down in growth, but these shrubs are quite accustomed to growing near other specimens. There may be some concern for chemical warfare at the rootzone, but it looks to be taking to the area quite well, for now.

https://www.gardeningknowhow.com/ornamental/trees/camphor-tree/camphor-tree-growing.htm

https://www.gardeningknowhow.com/ornamental/trees/crepe-myrtle

The tree's long roots may have been damaged as well. Construction can wreak havoc on nearby trees. Plus the additional water probably won't bode well. I suggest consulting an arborist who can assess the damage on site and give you a plan of action.

https://www.gardeningknowhow.com/plant-problems/environmental/protecting-plants-construction.htm

https://www.gardeningknowhow.com/ornamental/trees/camphor-tree/camphor-tree-growing.htm

I don't see why not. I wouldn't be surprised, though, if you get some camphor tree suckers. Their roots travel far and wide, so it's possible they were not all ground.