Thank you for reaching out to Clarizen for these questions. From Clarizen side, you do have multiple options to pull the Time Tracking data, such as:
Time Tracking Reports via the Reports Module (which can be sent to an email via Scheduled Workflow Rule
Time Tracking Reports via our Excel Add-In, which provides you more flexibility in the data you can pull and the format (in excel).
Using the Clarizen API
As for the Qlikview side, it all depends on how the data can be received, whether manual or automated. From the sounds of your suggestions/options. It accepts data via scripts that can be run but I do not have enough knowledge of the product to speak intelligently on it.
I believe you have two options to move forward...
1 - Speak with you Account Manager or Customer Success Manager on a Best Practice based on needs.
2 - Work with our Professional Services team to configure something via the API (if possible).
As an added item, I will repost this question in our Developer section where API questions are commonly handled.