My first thought was juniper but the last photo looks more like a cryptomeria. Either way the problem (and yes you're right there is a problem) might be that the lawn is growing into it and maybe the poor shrub is being weed whacked or hit with a weed or grass killer. I would carefully hand weed the grass out of there and water it well.

Tradescantia is pretty indestructible. Slice off the crushed part, brush the healthy cut end with cinnamon from the spice rack (it's an excellent anti-microbial), and stick the end back into the dirt. Do note that there are about a million different varieties of spiderwort. This one looks like Tradescantia fluminensis variegata...and also like it's getting a great deal of sunlight to make such pale leaves.

Very, very etiolated plant. Probably Aloe juvenna. It should be much more compact, and leaves darker green. In full su, they will color quite dark. Plant should be introduced to sunlight very gradually, especially one that is so "light deprived". Here is one of my plants, getting darker outside (even my plant could be still more compact - but it has been indoors for about 6mo, and I guess ligts were just ok, but not excellent): If my plant, I would cut stems (they can be cut into few pieces if desired) and re-root them. I would cut them quite short, since stretched plant will not revert to short one. They are quite easy to propagate from cuttings. Here are some rooted cuttings (left) and some cuttings (photo on right) that should have been potted up long time ago - but they are still ok, and hopefully I'll pot them up soon: Read thru -THESE THREADS- regarding 'beheading' succulents. Should you have any questions, ask...:)

growing trees indoors can be very tricky ... one trick is to use a media for trees.. which is not like yours.. a tree media sheds water and retains less.. as most trees prefer ... they are not water loving houseplants .. you almost treat them like cactus ... the other problem is light intensity ... indoors ... check out a bunch of these ... and learn all you can ... they make it sound like its the easiest houseplant in the world to grow.. so what do i know .... but if you start having issues.. remember what i said .... its the first 2 issues i would wonder about .... ken https://duckduckgo.com/?q=coffee+houseplant&t=ffab&ia=web ps: any green on a leaf means that leaf is still doing its job of converting light into energy... dont go cutting them off because they are ugly ... until it starts putting out new leaves to replace them ... in other words.. ignore your brown edged and boo boos... for now ...