There is an account limit of 1,000 Direct Messages sent per day. Once you reach this limit, you can’t send any more Direct Messages for the day. If you are sending Direct Messages to accounts that do not follow you, you may need to verify your phone number.
If you are sending duplicate Direct Messages to multiple accounts (including sending the same link to multiple accounts), this may be reported as spam activity and can result in you not being able to send a Direct Message for a short time. You may need to wait at least 30 minutes without any attempt at sending a Direct Message before you’ll be able to do so again.
Private direct messages won’t show up on anyone’s Twitter home page or public feed. They’ll only show up in the recipient’s Direct Messages list – and only if they follow you. You can’t send direct messages to people who aren’t following you.