on occasion yes.  Pretty normal especially if they're young before they get their 'egg parts' organized.  I get an occasional XX-large one every now and then.  I have one hen who always lays long skinny eggs that are pointy on both ends, and one who seems to often lay very round ones that are on the small side.  Neither would make it in a commercial set up. 

Yes, shell-less eggs occasionally happen but not often, if you have one that is laying them a lot, a practical person might cull her.  If feeding her doesn't bother you, then don't worry I suppose.

I put apple cider vinegar in my plastic waterers too, but NOT in the big galvanized one!!!  The acid in the vinegar reacts with the galvanized metal and chemicals leach into the water and that's not good for the chickens, plus, it causes the waterer to degrade faster which is bad too.

Honestly my biggest reason for doing it is it keeps the slime down in the water.  I'm not sure about the benefit to the chickens but our water tests out as borderline alkaline, so adding a little acid is a good thing for me IMO.  I've been told by many that cider vinegar is so good for them, but I can't swear that it's true, nor can I find it in Storey's Guide, but I haven't looked super hard in other places.  I'm quite sure it's not bad for them however as long as it's not overdone! 

Their comb color is in part a result of hormones and is also an indicator of their health.  When they're young, the combs are quite pale, when they start to lay, they'll get more red, when they molt they'll go pale, and if they are getting ill or if they're wormy they'll get pale too.

As far as poo goes, we can go on for days about poo!  What a topic!  Chickens have a sort of cycle… they'll poo 10 or so times what we consider 'normal' (and it's very good to have a grasp of what 'normal'.) Then they'll make what is called a cecal poo.  It's more, darker, and smellier than their normal droppings, but it's not quite runny, and it's normal.

WARNING LONG POST!!! 

OK, not everyone will agree with me on this, they don’t like to worm their flock too often, and I  understand that.  Years ago, we never wormed our birds at all.  We lost some to “failure to thrive” but  I think that was really in a large part to a bad worm problem, and if only 1 bird is sick from a worm infestation, you can bet the others are also sick but not showing symptoms yet.  If you see worms, either in the feces or the eggs, (yes, they can actually get into the egg if it's bad enough but that's pretty extreme) then you have a heavy infestation.  You will rarely ever see worms in the droppings otherwise.  Not even if they have a medium infestation.

DE and garlic or whatever is not going to ‘get rid’ of worms, though they may help as a preventative measure.

Some Chicken Experts (including poultry author Gail Demerow – i.e. Storeys Guide to Raising Chickens which I trust very much!) claim that if your birds are otherwise healthy they can tolerate a certain amount of worms and that it's better to keep a clean coop and yard and try to keep the worm population down naturally, than to subject the chickens to medication. It seems like the ecological approach of balancing pathogen and chicken so they can live in "harmony," but most people I know who keep chickens advise worming twice a year as a routine procedure.

For Wazine 17 (piperazine 17%) you use one ounce wazine per one gallon of water.  Or two measuring Tablespoons of wazine per one gallon.  Give that as their sole source of water for 24 hours.  Then remove from the coop.  Retreat in 14 days with wazine, or consider treating them with a more broad spectrum wormer like fenbendazole, levamisole, or ivermectin. (ivermectin is easiest to find here)

My personal feeling on worms does differ from that of Damerow.  I feel that it's best to worm twice a year and decrease the possibility of illness in the flock.  My first worming I use wazine and then during the necessary re-dose (you must always repeat piperazine worming) use the stronger wormer.  Then I use the stronger wormer twice annually for those birds thereafter.

New birds in the flock go through the wazine then stronger regimine unless they're chicks.  I worm chicks at five months with ivermectin and put them in rotation with the adults for twice yearly.

Parasites literally scar the digestive tract as they burrow into it and each scar in the digestive tract is one more place where nutrients can't absorb. 

Also, worms decrease the immune system of birds, steal the nutrients, irritate the digestive tract, make the bird more susceptible to other digestive tract illnesses by stressing the good bacteria of the gut, increase incidences of coccidiosis (even in adults), and spread to healthy birds.

Many people don’t like to do this, they feel it’s too harsh or not ‘natural’… if you rotate your laying hens yearly, which some people do, butchering or selling the older hens and starting new one’s yearly, then your hens probably won’t get a bad enough infestation to show symptoms before you ‘recycle’ them. 

I keep my hens longer though, so I aim for twice a year but in reality, it’s probably closer to three times over two years… yeah, I’m bad.  Over time, your property will get worms, worm eggs and worm larvae built up in the soil no matter what you do, and if you have other animals, that’s even more true.

I totally believe in ecological balance, but in keeping a flock of chickens in the same coop, on the same land, for years and years, (38+ years in our case) makes it so it's not possible to be truly balanced anymore, and we don't have a way to move the coop or chicken area!  If you wait till you see worms, you're waiting too long.

If that bothers you, and you have a vet who will test fecal samples for you without charging for a visit, you may be more comfortable with taking samples in to be tested to see how bad they’re affected.  That way it's less invasive and lets you know when to treat. 

(Wazine is relatively inexpensive, Ivermectin is rather expensive, but it goes a long way)

A weak one like that is all the more reason to start with the weaker Wazine and watch her…  I do want to say that wormer is essentially poison.  It's just a very specific one, but it can still be rough on a weak hen.  I agree with you that it may be your best bet, but it's still worth keeping in mind that it can be rough on them.

There's a product called Nutri-drench (for poultry) that may be useful as a sort of tonic.  It's not very expensive and it may give her an extra boost between doses.  Just a thought.  Last I knew Tractor Supply carried it.  I can't swear it's effective, but it may be worth having on hand if you can manage it… just a thought.

Edit to add// Also, if there's any question, I really suggest you at least talk to a vet about this.  I know mine do well with this, but if you have questions, do talk to your own vet.  I don't take chickens to the vet, I don't have that kind of money, but mine'll discuss this sort of thing willingly.