Welcome to tamatalk. Everyone here is willing to help you
I dont really know much about tamagochis, but i hope i helped.
#1 I dont think theres anything called the graduation party in v4. After you graduated from pre-school, you goes to school, after you graduated from school, you will be offered a job.
#2 If you have another tamagochis(v1,v2,v3 or v4), you can connect them and get them married when they are both adults(mostly four-years-old). If not, you can wait for the matchmaker to come. She will comes when your tama is six and above at the time 10.30am, 3.00pm and 7.00pm. You can set the time a minute earlier and wait for her to appear on the screen(e.g 2.59pm).
#3 When you have a baby and in the generation 2, the parent(gen 1) didnt died, s/he goes back to the tamatown. You can visit the parent/grandparent at tamatown.com or you can see them at the family/parent list in your tamagochi(the book icon). The items and points will remain the same. Mostly of the souvenirs are gone, but some remains.
#4 You need to connect to another tamagochi in order to make a friend.