Should I handle newborn kittens?

Newborn kittens. Image: MikeB

It should be very limited. I'll quote from an excellent resource, Cat Owner's Home Veterinary Handbook, 3rd edition:

"Most queens [breeding mother cats] display anxiety when their very young kittens are constantly handled by unknown people or if unfamiliar pets or other household animals [that] they are not comfortable with are allowed near the kittens."

This statement points to minimising contact with newborn kittens both by humans and other pets. Leave them alone but make sure the nest and environment is top class. You have to know what you are doing in cat pediatrics. It is a big skill and complicated. Seek veterinary advice promptly.

Newborn Kitten Care (comprehensive guide).

Socialisation later

After sex weeks social interaction with unknown human beings and pets such as dogs and exposure to new and nonthreatening situations are important for the proper development of the kittens. It's what makes them domestic cats and is essential for them to lead happy and well-adjusted lives in the human environment.

Sensitive Period of Socialisation for Kittens.