Before I go through each of your questions, a disclaimer: I came by my Spanish in Mexico and although I do have some friends from other parts of Latin America, I don't have a panoramic view of all Spanish speaking regions.
1) Regarding your example from Duolingo:
¿Bebemos leche nosotras?
I have never checked out Duolingo myself but this sounds contrived. I could only imagine myself saying this in a beginners' language class, or if I were trying to distinguish among several people sitting at a dining table, and the distinction happened to fall along gender lines. Even there, I'm not sure my listeners would get what I was trying to do. To me this sounds just plain awful because it's so hard to imagine a reason here to go against the natural omission of the subject. (The very formal word "beber" instead of the more natural "tomar" makes it grate on me even more.)
However, if we put some names or descriptions of people in place of the pronoun, then the question is not as bad, e.g.
¿Toman leche tus hijos? (context: I have invited your family to dinner)
However, for my regional ear at least, it would be much more natural to use question inflection with this word order:
¿Tus hijos toman leche?
2) How can the subject be at the end?
Before I give this deep thought and consider various examples, could you clarify, are you asking in what situations it's allowed to put the subject at the end, or are you saying that your instinct is that it would be weird to put the subject at the end and why did Duolingo do that? (Or something else entirely?)
3) Can I put the subject anywhere?
In principle, yes, as shown in guifa's answer. However, in practice, in my experience, we typically start by establishing the who or what we're trying to find out about -- most often the who. If you've ever been exposed to American Sign Language (ASL), this is analogous to how in ASL you start by setting up your cast of characters with each person occupying a particular position in your signing region, and then it being easy to refer to them briefly as you say various things about them.
Examples. In this scenario, I am imagining interviewing an older person such as a mother-in-law (using Ud. because of an age difference and also because that's how she was raised). when introducing some characters, I'll put them at the beginning to set up my cast:
Sus tías en el rancho ¿cómo aprendieron corte y confección? | How did your aunts in the country learn how to make clothes without patterns?
Once the cast is set, I don't need the subject:
¿Cosían todo a mano?
Bueno, y cuando se compró la máquina de coser, ¿cómo aprendieron a manejarla y lubricarla, si no sabían leer? No podían leer el manual, ¿verdad?
At this stage I can optionally include the aunts as a subject for extra clarity, and as guifa explained, since they're not the main focus of the question. (I would be rather likely to do this with an older person or a distracted person.)
They'll typically get tucked into the middle of the question somewhere comfortable. They could go here:
Bueno, y cuando se compró la máquina de coser, ¿cómo aprendieron sus tías a manejarla y lubricarla, si no sabían leer? No podían leer el manual, ¿verdad?
Bueno, y cuando se compró la máquina de coser, ¿cómo sus tías aprendieron a manejarla y lubricarla, si no sabían leer? No podían leer el manual, ¿verdad?
You can go with whichever feels more comfortable.
4) What are the rules for this? Is it only at the end or after the verb? What if it is not a pronoun but a name?
There aren't any hard and fast rules, as guifa explained. However, the longer the utterance, the less likely I am to put the subject waaay at the end. As for the fairly strict subject-verb inversion that English has, you can throw that out the window in Spanish. As a French speaker, I would think it would be an easy transition for you to get used to the subject-verb order with question inflection approach.
I don't think pronoun vs. name makes a difference.
5) Do these work?
(a) ¿Van al parque mañana ustedes?
Yes. But if we need a lot of words to refer to the park, or if the adverb gets long and involved, then putting the subject at the end would become very unlikely, e.g. ¿Van al parque mañana después de ir al súper ustedes? Yuck. We would leave out "ustedes" or we'd put it much earlier in the word order.
(b) ¿Van al parque ustedes mañana?
The following is okay but not the most preferred to my ear: ¿Van al Parque de los Patos y Gansos mañana ustedes?
(c) ¿Quiere venir a la fiesta María?
It's okay but most common for my ear is ¿María quiere venir a la fiesta? (Note, ¿Quiere María venir a la fiesta? is also possible but not the most common.)