Question 1: What did you get done today?
This is something that is routinely used in daily standups. With this question you can get a better understanding of the work that's got done on the day, and any problems, blockers that your co-workers are facing. It's useful when your whole team replies to it at least 2-3 times per week. If you notice that people are not replying to it, it's time to have a one-on-one meeting and then discuss problems.

Question 2: What will you be working on this week?

This is a great question as it requires you to prioritize what you want to work on this week. There may be 15 things on your mind, but you know that in a week you can only get the first 5 things done. And writing them down at the start of the week is a great way to help you stay focussed on what is important this week. Also, if this is visible to your whole team, then everyone becomes aware of the work that is getting done on the whole. Ideally you should set this question to go out on a Monday morning at 9:30-10:00 AM, at the start of the week.

Question 3: How is your week going so far?
This is a question to send out mid week - on a Wednesday afternoon. By reading answers to this question, you can gauge if someone in your team needs help, or re-arrange tasks if something is going to get delayed. This also helps your co-worker, as they have a chance to look back at their goals from the start of the week, and see if it is on track to finish by the end of the week. Usually, if someone is facing problems, or blockers that is stopping them from getting work done, it will show up here.

Question 4: What did you accomplish this week? sdsd sd sdsd 
This is a question that shows the actual work that got done at the end of the week. Did you have a productive week? Are you not happy with the work that has got done this week? By comparing the work that you were planning to do at the start of the week, with the actual work that got done, you can track actual progress, and re-asses tasks for the next week. As a manager, reviewing this also helps you identify outstanding performers, or people who need help. If someone is repeatedly not hitting the goals set at the start of the week, then you know that it is time to have a personal one-on-one, to help them do better work. Maybe they need help setting more realistic goals at the start of the week.

Question 5: In the last month, what was the work that you were the most proud of?
This is a monthly question that can be sent at the beginning of every month. It is a more high level question, asking employees to write down their most important work. By reading this thread, you and your whole team will get a better idea of how work is progressing for each person. You could also set up something, where one person from this thread is chosen, and their work done is acknowledged and celebrated in front of the whole team.

You can either ask any of these questions or all five of them. A good schedule is to start with questions 2, 3 and 4 - and then check feedback and improve from there.

Apart from the above 5, to improve team building you can include a few non-work related questions.

Question 6: What are you reading currently?

Question 7: Did you travel anywhere last month? Would you recommend it to your friends?

Question 8: What are the best movies, tv shows, youtube videos that you watched last month?

Question 9: What are your roses, buds and thorns? Roses are something that is beautiful and blossoming in your life, something that you are proud of. Bud is something on the horizon that you are looking forward to, and, thorns are problems you are facing right now

Question 10: What did you do last month? Did you do anything fun, why did you like it?

Question 11: What do you enjoy the most about remote working? What can we improve?
From the answers to this question, you can understand what you need to do to improve morale when working remotely. Maybe some co-workers are getting bored with the lonely, monotonous work-from-home setup, and you can help them by giving them a free coworking space which they can you when they want.

Question 12: Are you more productive working from home or office?
From this question you can understand if working remotely as a whole is net benefit to your company or not. Managers can use this to gauge if productivity as a whole has improved by working from home compared to office.

Question 13: Are there any team building activities that we should start?
While most team building activities are corny, getting all your remote employees to meet a couple of times a year at a resort can be beneficialy. If you allow them to bring their plus one, then they are a having a working holiday. Great for their family, and also for you as a team as everyone meets each other and have better relationships.

Question 14: Are there any other things we can add to make you more productive?
When people are working remotely, the communication among the team is less, and therefore you are not aware if someone needs extra help. Maybe sending them to a conference, or buying a paid course for them will make them more productive. These answers will come up in these questions.

Question 15: What's you remote working setup like?
This is a fun question for everyone to share pictures on what their remote working environments are like. Because remote teams hardly see each other, doing something extra is a great way to improve team bonding.

You can choose which questions to ask your team, and how often it should get asked. Ideally, you should ask these questions asynchronously, so that people are not disturbed and can answer in their own time.