They are most likely going through moult, during which time they will slow down or stop laying. This is normal for a hen in her second autumn/winter and will happen every year from now on. Feather loss can be quite major and very noticeable with half bald chickens running around or very light with just small patches of feathers or underfluff being lost.
They also need more protein in their diet to help replace their feathers, so that might explain the eggs getting pecked but that can also become a habit that is hard to prevent once they acquire a taste for it. It could also be as a result of thin shelled eggs. I have a hen that persistently lays thin shelled eggs and sometimes her eggs get broken and eaten but thankfully my girls have never developed a habit of breaking them and eating them deliberately.
Egg production should pick up as the days start to get longer. Some birds will start to lay again as soon as they have finished moulting and some wait until spring. Most will be somewhere in between. I've been getting just one egg a day and sometimes none for 5-6 weeks now (out of a flock of 17 laying birds) but a couple of girls are just coming back into lay now and I have 5 pullets that should be just starting to lay very soon.