How to select and copy some part of telegram message, one word, for example, without copping the whole message? And how to search telegram history matching half words? Now if I have message with text "1234567890", if I search history for letters "1234" - no messages are found :(
I don't think there is any way to do what you're looking for. It's up to the Telegram team if they want to allow parts of a message to be copied.
Similarly, the half word search is not supported on Telegram. You have to search with full words.
Telegram is an open-source project. You can talk to the developers on Github regarding your request.
Here is the project link - https://github.com/DrKLO/Telegram