Follow this input:
- If you have created a record on UI, then you need to click Submit for Approval to initiate approval process.
The record will be part of process if it matches with Entry Criteria and Initial Submitter which is defined in the Approval Process.
If you are going to submit record from Code or process builder, then you need submit for approval through code and same way process builder also provides options to submit for approval.
- If Manager (User record) record has valid email id and
Receive Approval Request Emails has chosen proper values then that user will receive an email.
You can go
Monitoring -> Email Log Files to track all the emails sent from Salesforce.
Email logs describe all emails sent through salesforce.com and can be used to help identify the status of an email delivery. Email logs are CSV files that provide information such as the email address of each email sender and its recipient, the date and time each email was sent, and any error code associated with each email. Logs are only available for the past 30 days.