1. The security for the log reader agent job is determined by what you selected for the agent security when creating the publication. In replication monitor, right click on the publication and select properties. Go to the Agent Security page and you will see the accounts setup to run the agents. You can also check the properties of the Run agent setup of the job, check the RunAs to see what account you setup.
One thing to note is that when setting up the security, in the screen for selecting the agents accounts, it's not recommended to run under the SQL Server Agent account. You would generally want to create separate domain accounts for replication agents.
2. Did you create the subscription or just create the publication? How did you create the subscription? For the subscription, you would want to check the snapshot agent to see if this was delivered, check the job as well as view the details of the snapshot agent in replication monitor. That would be the start of the replication process and when you would see the replicated data on the subscriber.