It is now possible to send messages to personal chat(1:1) or to group chat in Microsoft Teams using Microsoft Graph API. And yes, the messages will be displayed in the Teams application using Microsoft Graph API.
Please refer the "1:1 and group chat messages" section from the below microsoft documentation link:
chatMessage resource type
Also, below is the graph API to send a message to any conversation you want using Post HTTP method :
https://graph.microsoft.com/beta/users/{user-id}/chats/{chat-id}/messages
To fetch {user-id} and {chat-id}, please follow the below steps using Get HTTP method:
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Fetch the user id of a logged-in user or user id of other user using below graph API's:
https://graph.microsoft.com/v1.0/me
https://graph.microsoft.com/v1.0/users
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Fetch the conversation/chat id of a user:
https://graph.microsoft.com/beta/me/chats
https://graph.microsoft.com/beta/users/{id}/chats
As of now, there is no graph API to reply to a personal chat but we can reply to any team's channel message using Microsoft Graph API.