1. Is the 24-hours window for calculating a conversation configurable?

No, the 24-hours window is not configurable.

2. If the conversation is assigned to an agent, do we close the conversation when the agent marks the Chat Complete?

If the conversation is assigned to an agent, the agent can complete the conversation by clicking on Chat Complete, after which the conversation will move to bot state and it will be auto-completed after 24 hours, from the time the conversation began. However, if the conversation is in the Waiting for user state, as marked by an agent, then it will auto-complete after 8 minutes of inactivity. 

3. How much data is visible in the Analytics tool?

You can view upto 90 days of data from the present date on the tool.

4. If the customer is using a third-party agent chat tool (e.g. Salesforce, Zendesk, etc), is there a possibility to get a Conversation Split in that case?

If the implementation to the third party is done using TRACT, then Conversation Split number should be visible.

5. If the Enabled Human Assistance is on, will the broken messages section in Conversation Split will always be zero?

Yes, it will be 0.