Depending on which tool you're using, the answers to your questions will vary:
1. If you're referring to marketing emails that you've sent via the HubSpot email marketing tool, there are multiple factors that affect the processing/send time of a marketing email in HubSpot after you hit send: the scheduled send time, including the time of day, your email's place in the send queue, and size of the recipients list. Mid-morning is generally considered the highest-traffic sending time of day so processing delays of that size are not unexpected around the time of your send.
Additionally, our send times are largely limited by the recipients' email providers - they don't allow unlimited SMTP connections or volume: we try to get the emails out as fast as possible, but we're only one part of the equation.
You shouldn't, however, be experiencing any significant delays when you send 1:1 emails from the CRM. If the 1:1 emails that you send from contact records are not working as expected, I'd recommend to reconnect your inbox in your account settings.
2. Any clicks and tracked contact activity will appear on the contact record. You can adjust the filter on the contact record to make sure you're only seeing the information that's relevant for you: