Facebook – When you delete your Facebook account, will the messages you sent still appear in the inbox of those you sent them to

No. Each message is transacted with a unique email ID. The inbox for each user is independent of messages. i.e., the message you send is not linked and stored internally with the inbox of the receiver.

Each mail transaction like draft, inbox and trash act independently with regards to the email user. Hence, manipulating any message will only reflect your email.

At least no major service provides allow such cross deletion.

Any messaging system doesn't allow you to delete item from another's inbox by deleting your own. Gmail will treat a message as a thread. So if you have a message in the inbox and also have stored it in a particular label, deletion of that message from the inbox leads to deletion from label.

However, it does not remove from your friend's Facebook inbox, it's that simple.

If you delete your Facebook account permanently, it will ask whether to delete related post and other things. If you then select yes, it will not show any posts on your friends timeline. If you do not agree, then your posts will be available. Other users, however, can't find your profile/identity anymore.