Why do I keep getting random messages from emails?
Its called spam its coming to you as an SMS message through your cellular carriers email to text gateway. If you do not need to receive SMS messages from email accounts (some automated alerting systems may use this method), then contact your carrier and ask them to disable that at their gateway.
Why are my texts coming through as emails?
It sounds like your Apple ID is activated with iMessage and your “Start new conversations from” is set to your email address, instead of your phone number. To resolve this, simply navigate to Settings > Messages > Send & Receive and configure the settings to start new conversations from your phone number.