Nick here from Shopify. Great questions!
The best way for you to set a limit purchase quantity would be via an app from the Shopify App Store as this feature wouldn't be native to the Shopify admin. You can find some of the main apps for this below:
There are a couple of different ways you can set a shipping rate per item. It can be done natively through Shopify as well as via an app. You can edit your shipping rates in the Shopify admin via price or weight, so this method would require you to set the rates separately for each for this. Shopify has a helpful guide going into more detail about this which you can read here. The apps would allow you to set custom shipping rates for individual products should you wish to do it that way. The main difference is the apps would normally have a cost associated to them. You can see some of the main custom shipping rate apps below:
Hopefully, this helps and answers your questions as well as giving you the best next steps to take.
All the best, Nick