Are there any restrictions or expiration dates on packet communication charges for the SIM card of the AiryQonnect compatible device (AQ-E1)?

No, AiryQonnect is a subscription service that provides a package of all the elements necessary for air quality monitoring (sensor terminal, communication fee, visualization screen).
One year's worth of communications fees is included in your initial purchase, so you don't need to worry about communications fees restrictions or expiration dates.
If you wish to continue using the service in the following years, it will be automatically renewed.