Starting sentence without subject pronoun
"minor sentences are used more often in speech and tweets than in formal written English.
(. . .)
Looking forward to seeing you. (moodless clause)
In conversational exchanges in English, minor clauses and abbreviated clauses play an important part in their ability to realise initiations and responses to initiations"

As for the above explanation, I have run into some sentences without subject such as "Looking forward to seeing you." "Wanna talk?(Do you wan to talk?)" during messaging with people. I consider them very internet chatting-like expressions and not used in real life. Have you ever heard people dropping subject pronoun like this way when you speak English face to face?

Question

Starting sentence without subject pronoun
"minor sentences are used more often in speech and tweets than in formal written English.
(. . .)
Looking forward to seeing you. (moodless clause)
In conversational exchanges in English, minor clauses and abbreviated clauses play an important part in their ability to realise initiations and responses to initiations"

As for the above explanation, I have run into some sentences without subject such as "Looking forward to seeing you." "Wanna talk?(Do you wan to talk?)" during messaging with people. I consider them very internet chatting-like expressions and not used in real life. Have you ever heard people dropping subject pronoun like this way when you speak English face to face?

Answer

Yes. In colloquial speech this is common. Do it all the time.

(I.e. [We] do it all the time.)

It doesn't sound uneducated. It merely sound informal. If someone is using on the Internet, it does not sound like modern Internet chat, it just sounds like someone writing the same way everyone talks.

Answer

Yes, we do this all the time. "Looking forward to seeing you" is probably one of the most common, especially in writing. In speech, we might preface it with, "OK, looking forward ..."

Answer

Yes, for example:  'See you later'.