It is usually really hard to get all the broken off roots out, and it is probably not going to be a problem for the other plants. Putting one or more in separate pots is not a bad idea, but it may have to wait till it gets warmer again in the spring. Most cacti do not grow very much when it is cold and relatively dark so it will have a harder time overcoming transplantation shock. If for some reason you do have to put one in a separate pot, let it sit with its roots bare for at least a few days in a warm and dry place. Get some fast draining cactus soil from a local nursery or big box store and make sure that that is not too wet. If you can get your hands on some pumice, mix that in with the cactus soil. Perlite can be used as an alternative, but is not as ideal as pumice. Then plant the cactus in that soil at the same depth as it was previously planted. Do not water it - the new soil will have some moisture and that should be enough for the cactus for at least the first week or two - given that it is inside and not getting much light. If the cactus is getting tippy support it with a suitable stake, it is going to take time for the roots to grow out into the new soil and start supporting the cactus.
If the cactus is getting a lot less daylight than before that in all likelihood explains the thinning and color change of spines at the top. I am trying to see if they are a type of Cleistocactus or Echinopsis, but from the pictures I cannot really be sure. Cleistocacti do sometimes have thin new growth, but if it is an Echinopsis the thin growth almost certainly is indicative of too little light or a root problem.
Regarding the mix: stick your finger in it (without getting spines in your finger of course) and see what its consistency is: if it is pretty loose and granular that is good, if it behaves more like a single spongy mass it is probably not an ideal mix for your cacti. If it is spongy it might also still be pretty moist. If it is already too cold to keep your cacti in the window then you definitely need to reduce watering it - cacti actually can take a good amount of cold if they are dry, they will undoubtedly have trouble if they are cold and wet. Here in the Phoenix area - where most of the time we do not really get that much of a winter - a few nights around freezing maybe - I water my potted plants at most twice a month or if it rains (they are outside) not all.
Try to provide it with as much light as you can and if you feel that you have to water make absolutely sure that the soil is dry, if it still wet the cactus does not need to be watered. If the soil stays wet/moist for a really long time it is not a good mix for wintering cacti indoors, it probably is not a good soil mix for growing cacti.
