Can a 13 year old and 16 year old date if the 13 year old is born in 1998 and the 16 year old is born in 1995?

The birth years have nothing to do with anything.

Will the two ONLY date and not touch each other at all?

Umm, we can count. Not hard to figure out that a 13 yr old was born in 1998 etc.

In any case. There are no laws governing dating. However, 13 is a bit young to start dating one on one. The key here is the parents. If the parents (especially the 13 yr old's) agree to the dating then there should not be a problem as long as there is no sexual activity. Since a 13 yr old is under the age of consent in most places, any sexual contact, could get the 16 yr old in legal trouble.

If the parents DO NOT approve, then they both can be in trouble for defying the parents.

Yes, a 13 year old and a 16 year old can date. Years and ages have nothing to do with it unless you are planning to be intimate which in that case. No it is ageist the law.