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It is possible that the site they are in doesn't have the correct conditions for healthy boxwood growth, such as if the site has poorly drained or compacted soil or pH outside the proper range:
http://www.usna.usda.gov/Gardens/faqs/boxwoodfaq2.html

Boxwood can live in the shade, but will grow faster in the sun:
https://www.gardeningknowhow.com/ornamental/shrubs/boxwood/boxwood-care.htm

It is best to feed these with an organic 10-6-4 mix, if possible. Feed these in early spring. Here is an article with more information: https://www.gardeningknowhow.com/ornamental/shrubs/boxwood/fertilizing-boxwoods.htm

Here is a collection of articles on the care of these bushes: https://www.gardeningknowhow.com/ornamental/shrubs/boxwood/

I believe your suggestion of the 4-4-4 will be a good substitute. For a little more nitrogen, you can supplement with coffee grounds as well as a little coffee or tea mixed with mostly water. I do this for many of my plants that just need a little nitrogen. It is much better to underfeed than overfeed. Plus many plants like to be slightly underfed, as doing the opposite would be putting you at risk of salt buildup. Here is an article that will help: https://www.gardeningknowhow.com/ornamental/shrubs/boxwood/fertilizing-boxwoods.htm

It sounds like you have the right idea. Here is an article that will give you more information: https://www.gardeningknowhow.com/ornamental/shrubs/boxwood/trimming-boxwood-bushes.htm

There are, actually, quite a few things that can cause this problem. Typically, this is indicative of a root or soil infection. Many times, putting wettable sulfur into the soil area, and watering in will help. With more aggressive cases, this may not work, and you will have to narrow down the exact disease for treatment.

This article will give you some more information: https://www.gardeningknowhow.com/ornamental/shrubs/boxwood/yellow-or-brown-boxwoods.htm

This, actually, sounds like the indoor humidity being low, and possibly not receiving enough light. If you have another window that gets bright light all day, then you may want to move it to where it is bright but indirect.

It may be a battle until the temperatures remain mild enough to put it back out. Just keep caring for it, and when the temps get back up, it will grow new leaves. I don't believe it will die, but it might try and go semi-dormant.