How many emails can I send per day?

As of this writing, information on limits can be found  here for Gmail accounts and here for G Suite accounts.

If we detect that you've reached a Google quota limit we will pause sending for a period of time and then automatically resume later. However, do not rely on this detection to protect yourself from going over your quota because 1) we usually only get this notice after you've already exceeded your quota and 2) sometimes we're not able to make that detection fast enough to stop emails that are already queued up.

Your best bet is to use Mailshake's  sending calendar settings to limit how we schedule your messages.

Keep in mind, if you're sending via an alias, your Google limits apply but so also might any limits that the service that runs your alias email domain has.