iMessage sign out

Re: "iMessage sign out" : "sends with my email/Apple id" : "in group chats I can’t get the messages"

You may want to check that you are correctly signed in (to your iPhone) with your Apple ID:

Sign in with your Apple ID - Apple Support

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You may need to check you have listed yourself and your details in the Contacts app:

Use the + to add yourself as a new contact

or

1. Tap your name in contacts, then tap Edit.
2. Enter or update your contact information.
3. When you’re finished, tap Done.

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Re: "when I text or sent messages it sends with my email/Apple id"

See if Apple support's online article (link below) can help:

How to: Add or remove your phone number in Messages or FaceTime - Apple Support

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Re: "in group chats I can’t get the messages even if they have sent messages "

Check out: Have a group conversation in Messages on iPhone - Apple Support

iMessages go by wi-fi between Apple devices, yet Messages uses SMS / Text with Android devices :

You may need to check you are allowing Messages to use cellular data

(charges may apply, depending on your plan / provider)

View or change cellular data settings on iPhone - Apple Support

Eg:

"Go to Settings > Cellular, then turn Cellular Data on or off for any app (such as Maps)

or service (such as Wi-Fi Assist) that can use cellular data.

If a setting is off, iPhone uses only Wi-Fi for that service".

You can use Wi-Fi Assist to automatically switch to cellular when you have a poor Wi-Fi connection

More Info: About Wi-Fi Assist - Apple Support

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If you still need help:

You may want to sign in to your Apple ID account online, and check all your details are up-to-date:

Apple ID account sign-in online: https://appleid.apple.com

If needed: Get a verification code and sign in with two-factor authentication - Apple Support

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Messages Support webpage: (info. / support / contact options etc.)

Messages for iPhone, iPad, Apple Watch, and Mac - Official Apple Support

All the best :-)