Can I use forms inside Teams to automate surveys at intervals?

One thing I'd add is to make it a group form owned by the team rather than a personal one, so the schedule and results don't break when someone in HR changes roles. Keep that same form open across cycles and add a simple "Which month is this for?" question, otherwise it's easy to get muddled responses if someone answers late. In the flow, set the recurrence in your local timezone and post to a dedicated channel rather than lots of individual chats, so people can find the current survey without digging. If you do want targeted reminders, you'll need to collect names, which is the trade-off against running it anonymously. For a quick trend view, sync the responses to Excel and filter by that month field, rather than starting a fresh form each time.

Forms itself cannot schedule or send reminders, but the three things you want are all doable with Power Automate, and for monthly pulse checks there is also a purpose-built option. The simple setup:

• Build the survey once in Forms and keep using the same form every time. All responses collect in one place, and every response has a submitted date, so comparing months or quarters is just a matter of filtering the linked Excel sheet by date. Add a short question such as Which month is this for, if you want an explicit label.
• Create a scheduled flow in Power Automate with the Recurrence trigger (monthly or quarterly). Add the action Post message in a chat or channel in Teams with the link to the form, so it lands in the channel or in each person's chat at the right time.
• For reminders, add a second scheduled flow a few days later. It reads the responses (Forms action Get response details, or the Excel sheet), compares them to your list of people (a group or SharePoint list), and sends a Teams message to anyone who has not answered. Note that this only works if responses record the person's name. If you need the survey anonymous, you can only send a general reminder to everyone, because the form cannot tell you who has not replied.
• Optionally, send a summary of the results to HR from the same flow after the deadline.

If your goal is regular employee pulse checks specifically, look at Viva Pulse. It is built for recurring check-ins, handles the scheduling and anonymity, and shows trends over time in Teams, so you would not have to build the flows yourself. It needs the right licence, so check that first.