Q:

Verbs and pronouns in action phrases e.g. me: *smiles*

An action is usually a verb phrase surrounded in asterisks to show that someone is doing something. When an action is written, why is it using the third person verb conjugation even though the subject is in the first or second person? It doesn't feel right if I use the first or second person verb conjugation. I know that it can also use the gerund form of the verb. But the gerund can be used with any subject.
For example:

me: *smiles* (common)

me: *smile* (doesn't feel right)

It's quite commonly used in memes. Example
It's also found in texting while performing an action or role-playing.

*blushes*

Other examples can be found by searching 'role play texting' on Google Images.
And also why does it use the object form of the pronouns and not the subject form? It also doesn't feel right if I use the subject form of the pronoun,
Example:

me: *smiles*

I: *smiles*

Why is that the case? Has it been this way since a long time ago or is it only done now because of the internet?

A:

These "asterisk-bounded autonomous stage directions" are a mashup of traditional playwright conventions and modern internet ones.
Like traditional stage directions, they exist outside of the characters' first-person dialogue and are therefore in the third person. They also display the brevity of phrasing, unique typographic demarcation, and "viral-ness" that the internet craves.
In The cyberpragmatics of bounding asterisks, Language Log's Ben Zimmer summarizes:

. . . by giving yourself your own stage directions enclosed in
asterisks, you treat your own words as lines in a play, and then step
outside of your character to give the perspective of the playwright in
the play you're acting in.

As for the origins, Mr. Zimmer explores "the use of bounding asterisks to signal non-verbal noises or actions as a kind of self-describing stage direction." He points to comic strip caligraphy as an influence, and notes that:

The origins of such usage likely can be found in text-based
role-playing games in MUDs (Multi-User Dungeons/Domains), which were
superseded by IRC and instant-messaging interfaces. As one "Role Play
Manual of Style" explains, "Actions are enclosed in asterisks and
written in third person perspective." But this type of asterisking has
thoroughly infected Usenet posts, blog comments, tweets, and anywhere
else online that people feel the need to describe real-world actions
in a virtual space.

As for the use of me instead of I, forget about subject and object personal pronouns and instead think of me as a name—a proper noun—that you call yourself.
References:
The cyberpragmatics of bounding asterisks
Asterisks > Computing > Computer Interfaces

