I am a corporate technology lawyer experienced in setting up venture funds and acting fur funds in their "portfolio" investments. Always happy to see new innovative approaches to investment funds. The above offering can be done. I suspect it would require more "maintenance" on the fund level and investment level but definitely do-able.

I work with several start-ups in the "space" and have sold three Health-Tech clients to large US corporations. The above listed items are typically covered in the type of services I provide.

One would need to review the sale agreement to provide you with any sound advice. If properly drafted in first place (ie protecting your right to future payments) then there should be some contractual tools available for you in the agreement.

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.

They do and they have. I like the concepts of tech investments brought in by US angel investors in ME seed deals.

I'd probably spend 30m with an experienced lawyer to make sure that the 'standard' meets your needs. Despite startup, lean, etc. you don't want to look stupid.

Type of shares are generally split into two: common/ordinary (depending on the jurisdiction) and preferred. The former are granted to founders and employees (most commonly as options with a right to purchase common/ordinary shares). The latter are generally issued to investors and include special rights such as liquidation preference, anti-dilution protection, etc. Preferred shares reflect the fact that the holder (investor) has paid a premium in consideration for issuance of such shares. Don't forget to consult with a lawyer.