RE: Daily maximum API calls reached

"API calls", and "API connects" are different.

API connects are how many conversations the bot had through the API. This include your application id, and other application ids.

API calls is the number of API calls for your application id. An API call could be a connect to a bot, or a message to a bot, i.e. each message is an API call (a conversation can have many messages).
To see your API calls, go to your user page and click on "Details".