Is there any limits on Outbound Messages for each Workflow Rule per day? If there are, how many per day/per object? Is there a total limit per organization per day?
As per Documentation there is no limit for Outbound message per day. From what I am aware there isn't a limit on the number of outbound messages sent. API limit is only for incoming API calls. Outbound Message and APEX Callout is not counted in this limit.
note that despite being on "Unlimited Edition" you are limited in the number of API calls that you can make, this limit is 5,000 per user licence within any 24 hour period. (Unless you have had this amended by arrangment with Salesforce).
If you look at Salesforce Developer Limits Quick Reference | Workflow Limits:
The immediate actions and each time trigger can have:
- 10 email alerts
- 10 tasks
- 10 field updates
- 10 outbound messages
- 10 flow triggers2
So it seems the only limit on outbound messages is number of callouts per rule.