I am a lawyer experienced in drafting and negotiating licensing agreements. I'll try to address your question and points made therein through the following brief notes:
1. You should consider having an agreement, in the form of a software license or software subscription agreement (the latter applicable to SaaS model), not only for the released product but also for you Beta version (the "Beta").
2. Such an agreement should clearly state your ownership in your software and the specific licensing terms (whether Beta or "production" version); such terms would address restrictions on transfer and re-distribution.
3. I would include terms regarding limitation of liability, confidentiality, use of data and exempted warranties.
4. In a Beta context I would recommend clarifying (in the agreement) the following points: (a) you will have no liability for any harm or damage arising out of or in connection with the use of the Beta; (b) use of the Beta is for evaluation purposes only and may not be supported; (c) the evaluation is for a limited time, you may discontinue the Beta at any time and the user may loose all their data inputted during the trial period; and (d) any usage information regarding use of the Beta , such as results, comments, or suggestions should be deemed non-confidential to the user and usable by you.
Please note that the above notes are based on very limited background and should be examined in the context of the specific facts. Happy to get on a Clarity call and further discuss this matter.