Only iDevices can send and receive iMessages. If you want your phone to receive text messages, people must send those messages to your mobile telephone number.
You can ensure this happesn (more or less) by making sure you are INITIATING all messages as if coming from your mobile number. Go to Settings > Messages > Send & Receive. Be sure your mobile number is listed as a way to reach you on iMessage and also be sure the option to "Start new conversations from:" is your mobile number.
iMessages communicates exclusively to other Apple devices.
When you send messages on your phone, you are sending SMS text messages. Your phone can probably receive SMS text messages as well, that's really up to your cellular carrier. Your iPad can neither send nor receive SMS messages.
Your iPad can receive replies to messages sent on your phone if both these are true:
- The person sending the reply is using an Apple device
- Your iPad is set up to receive replies using an address also used by your phone