
No one seems to have answered yr questions, so I'll have a go, altho' Chis are not my breed:
1. Ask your Vet. Pups usually have 2 initial innocuations
2. Pet plan seems to be the most popular choice. have a look at this forum - loads of discussion on insurance recently.
3. Don't know of any other health things for Chis - again ask yr vet or contact your breeder. If the breeder isn't helpful, go elsewhere. Oh, worming is important - breeder should tell you how & when.
make sure you've got some of the same food the breeder had the pups on - don't change food suddenly.
4. Your pup can go & stay in house with another dog, but it's not really advisable. Depends on circs really, but if the older one goes out & about, he could bring an infection back, without showing signs of having it himself (he will be immune). Anyone who already has a dog is taking the same risk if they bring a puppy home.
Have you tried asking yr breeder these things? I'd be a little concerned that she is having 2 litters so close together, but then Chis do have smallish litters & maybe she has a good reason for doing so. BUT if she doesn't want to answer yr questions, warning bells should start ringing.
HTH