I've raised young birds in some very cold temperatures. However, in answer to your first question. It depends on your purposes with your flock. In general, it's best not to hatch pullet eggs for several reasons.
I posted this in another thread.
"Here's all I know about the subject.
It is true that many people hatch from pullet eggs all the time with no problems.
It's also true that the smaller chicks from small pullet eggs will usually catch up in size by a year or so.
So what are reasons not to do it?
A chicken deposits about 6 grams of calcium carbonate and thus 2.5 grams of elemental calcium in an egg shell- regardless of age. So a pullet egg shell will be thicker than one from a mature hen and possibly more difficult to escape from.
There is clearly less albumen and a smaller yolk. That means less nutrition. Mammal babies can get all the nutrition they need from the mother and the abdomen can grow to accommodate. Once that egg is laid, that's all the nutrition and space there will ever be.
I've had old timers tell me that continuing to hatch from pullet eggs will decrease egg sizes in subsequent generations.
On the other hand, albumen quality is better with young birds than older hens.
IMHO it depends upon how big the egg is supposed to be based on the breed. Eggs from the breed I raise are supposed to be 65 grams or larger. I've always tried to set eggs that were 55 grams or larger.
Then I had a predator massacre and only 3 mature hens survived. The pullets had just started laying eggs so I decided to set every egg I could get reducing my low weight limit to 45 grams. Now that those birds have matured (they're almost a year old), I see the results. Unlike past generations that started laying larger eggs by about 8 or 9 months of age, the eggs are still in the small/medium/large range rather than the XL and jumbo they should be by now.
That probably wouldn't matter to most backyard chicken people or even noticeable to those with multiple breeds. But since I've eliminated all other breeds, it's very noticeable to me. And since I'm breeding to a standard, egg and bird size is an important part of that standard.
I'm now paying much closer attention to egg size when I set and track results through adulthood and generations to follow.
I group eggs by sire, egg color and egg size. I'm tracking eggs in the 50-55 gram, 55-60 gram, 60-70 gram and 70+ ranges. In those ranges I'm checking hatch rates, chick survivability and weights. I'm weighing every 10 days for a month then monthly. In adulthood these hens are supposed to be 4.4-5.3 lbs. and cocks 5-6.6 lbs. I had been shooting to be at the high end of that range so we'll see what the future holds.