Hello,
What I observe in the photos are mature trees with nowhere to go. There is simply not enough room for their root system, and likely the poor drainage is contributing to root rot and general decline. Once a tree begins declining, it becomes vulnerable to other diseases.  It sounds like your trees may be affected by tip blight. This can be a problem with trees that do not have good circulation around them, and between the trees being very close together and seeming to have a wall behind them, I suspect they do not get adequate circulation. For information and tips on identifying this disease click here:
 https://ag.umass.edu/landscape/fact-sheets/arborvitae-needle-blight
If you see the black dots on the foliage, you could try pruning out the affected foliage and twigs and try using a fungicide next spring as a preventative. Avoid pruning when the foliage is wet, and keep the foliage dry when watering the tree, by watering at the base and not spraying the water. 

If you value the trees more than the hardscape, you could remove that wall and put in a berm to give the roots more room, but I am not sure how successful that would be or how long it would take to turn their health around.  It may be time to consider planting something there that fits the available root space. 
I hope this is helpful. Thank you for contacting Ask Extension.
Ruth

Hi Ruth,

Thank you so much for taking your time to reply my questions. 

I have a few additional requests that I would greatly appreciate your input on:

1. I have attached a picture showing various leaf conditions, ranging from healthy to dead. I am curious if these pictures help to confirm if it is Needle blight.

2. The trees may not have been fertilized for the past five years. I am wondering if applying fertilizers could help in this case.

3. Upon reading the article on Needle blight, the use of fungicides is suggested. Should I apply the fungicide now, or would it be better to wait until fall?

4. Another recommended step involves pruning and discarding infected plant parts. Upon inspecting the trees, I fear that I will have to remove too many leaves, which may expedite the tree's death. Would you recommend chemical management instead?

5. You recommended removing the side wall to provide the tree roots with space to breathe. Could you clarify whether you are suggesting the removal of the small brick wall on the right in the attached image, or the one on the left where there is a tall patio?

Sorry for asking so many questions. 

Regards,

U Karki

Hello,
Here are my answers to your questions:
1. For a definitive confirmation of disease, it would be best to send it to the MSU Diagnostic lab.  Here is a step-by-step explanation of how to collect, package and send a sample into the lab. 
 https://www.canr.msu.edu/pestid/submit-samples/herbaceous-plants   This sounds extreme, but frankly it is easy, inexpensive and definitive.  It does look like a fungal blight, but without seeing the fruiting structures I cannot confirm that.  That said, this does not usually need treatment. Improving the over-all health of the tree may be enough. Here is an article that show the fruiting bodies- you may be able to see them .
https://www.missouribotanicalgarden.org/gardens-gardening/your-garden/help-for-the-home-gardener/advice-tips-resources/insects-pests-and-problems/diseases/needlecasts/pestalotiopsis-tip#:~:text=The%20blight%20usually%20starts%20at,fruiting%20structures%20dotting%20the%20surface.
2. Fertilizing may not be a good idea at this time.  With the restricted space of the root system, you are likely to burn the roots and stress the plant further.  It would be best to take a soil sample and get that tested here: https://homesoiltest.msu.edu/
If you find that you need some fertilizer, it is best to fertilize in the fall after the first frost and before the ground freezes, usually October timeframe. It is always best to determine what is needed before fertilizing.
3. Fungicides always need to be applied preventatively. This usually means in spring before new growth emerges fully. Once the growth is infected with a fungus, fungicide will not "cure" it. It needs to be applied when new growth is emerging in spring. 
4. I would wait to prune until the health issues have been diagnosed and addressed.  Once you start getting new growth coming in, it will be easier to see what, if any pruning needs to get done.  Arborvitae typically self-prune older growth, so may not need to be pruned at all.
5. I was referring to the low brick wall on the right.  That seems to be restricting the roots pretty dramatically.
I hope this is helpful.
Ruth