Looks to me like the sort of feather loss usually associated with commercial layer breeds and their immediate descendants if cross bred. I think these hens get defeathered by roosters because a higher percentage of their intake of protein goes to the eggs than many other breeds. They thus tend to be rough feathered and their feathers break easily, they moult hard and long, etc, unless kept on generally a fairly different diet than what is recommended for two eggs a day layers or those hens known to produce over a hundred eggs a year. Other breeds don't usually show bare patches when moulting because the lost feathers are being replaced in the correct time to avoid that.
As for garlic, I give them a clove per bird per day on average. They can eat a lot more than that but even in adult humans a raw clove of garlic a day can help many problems, so it's potent stuff if you've got a good source. The active antibiotic property in garlic, Allicin, is created by the enzymes released when the clove is crushed, s I mince it for them.
If they're not allowed to freerange at all I would probably treat them a bit more thoroughly since any lice levels would be more easily able to build up, for example when one hen dustbathes and another one follows the second would be potentially picking up some lice the first bird rid herself of, being a closed environment. You could probably find some other threads with info on what other people recommend putting in dirt bath areas, I've used ash (from non treated wood) and agricultural lime, as in the stuff they feed to animals, and coarse diatomaceous earth. I think a lot of people use the pool-filter-grade D.E. and therefore have little results. It comes in various grades and I would seek a brand specifically used to worm horses or other livestock, not what you can get from the local pool supplies joint.