You may simply have to reactivate iMessage and FaceTime, but steps below and within the links may assist prior to resetting:
https://support.apple.com/en-us/HT207006
https://support.apple.com/en-us/HT204065
1) It appears your group messages are going through as SMS vs MMS. Check your settings in Messages. Correct as needed. (Settings - Messages - )
See explanation below and additional information that may help:
If no info or steps herein assist, contact your carrier. It could be a server issue, for example or they may simply need to reset an option, etc....
These messages may appear in green text bubbles and go through your carrier. Group SMS messages don’t support multimedia attachments, like photos or videos.
--------》 All responses in a Group SMS are sent as individual text messages and the recipients can’t see the other responses from the group.
Learn how to send and receive iMessage, MMS, and SMS messages on all of your Apple devices.
- Open Messages and tap
to start a new conversation. - Enter the recipients' names or tap
to add contacts. - Enter your message, then tap Send
.
To send a group MMS message on an iPhone, make sure MMS Messaging is turned on. Go to Settings > Messages and turn on MMS Messaging. If you don’t see an option to turn on MMS Messaging or Group Messaging, contact your carrier to see if your plan supports Group MMS Messaging.
You won't see read receipts in group messages.
With Tapback in iOS 10 and later, you can quickly reply to messages with expressions, like a thumbs up or heart. To reply with a Tapback:
- Open Messages, and tap a group iMessage.
- Double-tap a message bubble or photo.
- Tap one of the six responses that appear to reply to the message.
To see who sent a Tapback, just tap on the Tapback.
Have multiple group iMessages? Name your group iMessages so they're easier to find. To name your group:
- Tap a group conversation, then tap
. - Tap Enter a Group Name.
- Enter a name, then tap Done.
You can name only group iMessages, not MMS group messages.
Anyone in a group iMessage can add or remove someone from the conversation. You can remove a person from a group iMessage that has at least three other people. You can’t add or remove people from group MMS messages or group SMS messages.
- Tap the group conversation you want to add someone to.
- Tap , then tap Add Contact.
- Enter the contact information for the person you want to add. Then tap Done.
- Tap the group conversation that has the contact you want to remove.
- Tap , then swipe left over the name of the person you want to remove.
- Tap Remove, then tap Done.
Are you getting too many notifications from your group? If you don’t want to leave a conversation, you can turn on Hide Alerts:
- Open Messages and tap a group conversation.
- Tap .
- Turn on Hide Alerts.
When Hide Alerts is on, 
will appear next to the conversation. This stops notifications only for that message conversation, not your device. You'll still receive all other messages and see notifications for them on your Lock screen.
To leave a conversation, tap Details, then tap Leave this Conversation. You can only leave group iMessages that have at least three other people.
******OTHER*******
If you have issues with a group message
If you’re in a group message and stop receiving messages, check if you left the conversation. Open Messages and tap the group message. If you see the message You left the conversation, then either you left the conversation or you were removed from the group message. You can rejoin a group message only if someone in the group adds you.
You can also start a new group message. Here’s how:
- Open Messages and tap .
- Enter the phone numbers or email addresses of your contacts.
- Write a new message, then tap
to send.
If you have other issues with a group message, you might need to delete the conversation and start a new one. To delete a group message:
- Open Messages and find the conversation that you want to delete.
- Swipe left over the conversation.
- Tap Delete.
When you delete a message, you can't recover it. If you want to save parts of a message, take a screenshot. To save an attachment in a message, touch and hold the attachment, tap More, then tap Save.
