Appointments scheduler linking to Google Calendar

Hello,

I am thinking to use your plugin to create a new platform where people book appointments with providers (typically time slots, 1, 2, 3 hour sessions etc.). I will have multiple providers, each will need to have their own availabilities. They will need to set their schedules (i.e. the days of the week that they work and the hours each day), this will form their base availabilities. When someone books an appointment with them, it will obviously need to make them unavailable for this period so that they cannot become double booked. My question is, what would be the best way to tackle this with formidable forms?

Service providers and appointments would be custom post types. How would you recommend to tackle the part where we only allow providers to be booked when they are actually available (i.e. taking into account their schedules as defined above, and any appointments that have been booked for them).

Would it also be possible to link each service provider's availability to a Google Calendar, so that any time they are booked via our service it updates their Google Calendar and also if they are booked outside of our system, any blocked availabilities in their Google Calendar must also be respected when a user tries to book them via our service.

Thank you in advance!