The blue is not fungus, its residue from fungicide thats been used before you bought the plant. Many fungicides leave a blue or white powdery residue. Nothing to worry about other than that it's toxic if it gets ingested, licked by cats.... In production they keep them very humid and will use fungicides to keep the leaves in pristine shape for sale as the tips often go brown. They should use a mild detergent to clean them for sale. Cordylines also often shed lower leaves when placed in a new environment especially a much drier one. This is also not something to worry about, though you could improve humidity one way or the other. Look at the roots if they are nice and white thus healthy it's not a root problem. Root or stem rot will cause the lower leaves to drop off very quickly. It's unlikely this is your problem indoors though.

Older leaves will look spotty and brown parched, before they abort, also no problem.

However the large "water mark" in the healthy pink leaf is symptomatic of something, probably dry air in your case or possibly over watering, no drainage at the roots, or even lack of water at the roots, check all these things. It could also be burnt from being too close to a window or a lamp. To increase humidity sit the pot on some pebbles in water don't over water instead. They do like a moist soil but not a boggy one. Indoors they also want the brightest light possible short of actual sun, certainly in summer as the leaves can scorch through glass. The leaves are thin in most cases and burn easily or dry out easily especially the new leaves. Also don't feed more than just a tiny amount once a year indoors.

Cordylines quite frankly don't make the best house or office plants because they love humidity and warmth so much and because the leaves are most often quite thin. To recreate ideal conditions would make anyone using the room uncomfortably steamy. However if your climate is good you can place them outside for a few months (even just summer) then inside for one, rotating them as you go, or just inside for winter. Other wise look for the varieties with the thickest leaves to try, there are one or two that with some help should do better as a result. Off hand C. fruticosa "Vanuatu" is one, shiny largish jet black leaves, arranged beautifully. I've never had any problems with it's leaves outdoors in full sun and drenching rain, humidity and a dry warm winter. Some of the rounder paddle shaped small ones or the larger leaved reds with the same thick leathery leaves might also do.

Dracaena are all round are far better than Cordyline fruticosa for permanent indoor use.

You are unlikely anyway to get a fungus problem on the foliage indoors only possibly at the roots or the cane. Fungicide could help with that but then it must be mushy wet and black to be that. Lower older leaves don't always look their best indoors but it is technically better to wait for them to drop off rather than cutting them off or the plants stem (cane) might get thinner and thinner in the process, bending over and ultimately die.

Hope they've survived meantime anyway!