1. There is an automatic trust relationship that is established between parent and child domains. In order to give users from one domain access to resources in the other, you just need to give them permission.
For example, if you look at the file permissions for a folder in the child domain, you can add a new user, browse to the parent domain, select the user or group that you want from that domain and then select the appropriate permissions.
2. If the parent DC goes down, users in the child domain should be unaffected, as long as there is a DNS server in that child domain that they are configured to use, and there is a GC that they can access. The only thing they will be missing is the schema master and the domain naming master. Schema is only needed if you are making changes to the schema, and domain naming is only needed if you are adding or removing domains from the forest.
Also, users will be unable to access any resources in the parent domain that they might have access to, but that is expected. They should be able to function within their own domain with no problems.