I just went and looked at Feather Lover Farms website.
Based on the website, and the USPS website, and what you've said:
I think part of what happened is just normal but your research had not prepared you for it, but I also think they were providing substandard service in some ways.
They have a "live arrival guarantee"-- which means they guarantee that the correct number of chicks (in your case 3) are alive when they reach you (they were). This is fairly common among hatcheries: it's their business to get the chicks to you in good shape, and your business to take proper care of them after that.
The obvious problem with a guarantee like that is you don't have any recourse if the chicks arrived alive but then do poorly even when you take good care of them. That could be the hatchery's fault, or the fault of the way the Post Office treated them, or sometimes the fault of a new owner who didn't do enough research (I'm not accusing you of that, just saying it happens to some people.)
Some hatcheries ship for more of the year than others.
It is partly based on where they are shipping from, because a northern hatchery doesn't want to send out chicks in the middle of a snowstorm.
And it is partly based on when most people want to buy chicks, so the hatchery doesn't waste their effort hatching chicks earlier than people want to buy them. People often wait for nice spring weather before they get chicks, and that happens in different months depending on where they live in the US.
Shipping chicks in very cold weather or very hot weather has more risk than shipping in moderate weather. So if a hatchery starts shipping in March, and stops in June, they avoid the worst of the cold winter, the worst of the hot summer, and the fall when few people would be ordering chicks. But that isn't as convenient for people who DO want chicks at those times!
The only way they could "wait" would be to send your chicks to someone else, and send you chicks from a different hatch date. The chicks absorb the yolk right before they hatch, which provides enough nutrients for about 3 days. So shipping them a few days later would practically guarantee them arriving dead. (USPS policy also requires that chicks be under 24 hours old when shipped, for exactly this reason.)
The Post Office has a list of exceptions, when they will not give a refund if the package is late. "Live animals" is one of the exceptions.
https://pe.usps.com/text/dmm300/604.htm
So paying for upgraded shipping may not be worth the money. (There is another hatchery, I forget which one, that has a page talking about exactly that: it's not worth the extra money, because the chicks don't arrive any faster, and the Post Office won't give any refunds.)
That is completely normal for any chicks, from any hatchery, shipped through the Post Office. Better tracking would be really nice, but choosing a different hatchery won't help
That is definitely poor customer service.
Also, their website states,
"Heat pack(s), plenty of nest material under and/or around the chicks and professional packaging are included with the cost of shipping."
https://featherloverfarms.com/pages/feather-lover-farms-faq
So leaving out the heat pack was not right, unless they had specific reason to think the chicks would do better without it in those specific circumstances.
But three chicks did arrive alive-- so maybe they were right to pack them that way in this case. (A heat pack and 4 cooked chicks would not have been any better, but a heat pack and 4 healthy chicks would have been much better. I have no idea which would be the more likely outcome with a heat pack in this case.)
Lavender should have been pretty pale in color too, so it might have looked yellow. If you've got photos, someone here might be able to pick out the lavender. If they did not send it, then logically they owe you a refund for at least the price difference between it and what they did send.
I've never heard of a "death gene" in lavenders of Silkie or any other breed, but that could just meant that I haven't looked for information in the right places. If that is true, it might explain why the lavenders are priced higher than other colors on that site.
Yes, their prices are very high compared to many other hatcheries.
They say their silkies are very good quality-- if that is true, they may be worth that much, for people who care about those details (like taking them to a chicken show). But for people who just want cute pets, I would consider them overpriced. And I don't know if their Silkies really are good quality or not.
If they are shipping unhealthy chicks, then yes it would probably happen again if they ship new chicks. If they shipped healthy chicks and the storm + Post Office caused the trouble, then new chicks might be fine.
And that is why I'm explaining some of these other details, too.
Hopefully some other newbies can have a better idea what to expect, and avoid the heartache and lost money.
You've had quite an unpleasant introduction to ordering chicks

Hopefully things will improve with your new ones that do not have to be shipped