Add a letter to me, and you'll be thrown into medieval times,
Take one away, and your stomach may be doing this.
If you meet one like me, they will never commit any crimes.
I can be used as the bare minimum, a near miss.

I'm the the height of action, the very definition of it.
Or I can be how someone styles their hair.
The ability to perform, so you are not going to quit.
With an e, and I become a female deer.

Neither male or female, I'm neutral as can be.
With an l, I'm cool and hot simultaneously.
Be wary though, I'm a frightening movie,
Add a couple letters, and I move spontaneously.

What am I?

Just Do It

such that

Each verse corresponds to one of the words

Add a letter to me, and you'll be thrown into medieval times,

Just $\rightarrow$ Joust

Take one away, and your stomach may be doing this.

Just $\rightarrow$ Jut

If you meet one like me, they will never commit any crimes.

A just person behaves according to what is morally right and fair.

I can be used as the bare minimum, a near miss.

Just can mean barely or by a little.

I'm the the height of action, the very definition of it.

Do, means to perform an action.

Or I can be how someone styles their hair.

A hairdo

The ability to perform, so you are not going to quit.

Do means to achieve or complete.

With an e, and I become a female deer.

Do $\rightarrow$ Doe

Neither male or female, I'm neutral as can be.

"It" is a gender neutral pronoun

With an l, I'm cool and hot simultaneously.

Lit is slang for cool and can mean alight also.

Be wary though, I'm a frightening movie,

It, the Stephen King novel and subsequent movie.

Add a couple letters, and I move spontaneously.

It $\rightarrow$ Itch

Title

It's three words long and is the motivational trademark of Nike.

• Well, the last clue wasn't quite what I had in mind, but that's okay. Great job – Joe-You-Know Jul 13 '18 at 15:41
• Aww nuts. Sniped. I'm too slow at typing, I guess. – Ian MacDonald Jul 13 '18 at 15:44

You are

Just Do It

Add a letter to me, and you'll be thrown into medieval times,

Joust is a kind of battle in medieval times.

Take one away, and your stomach may be doing this.

Jut is what your belly might do if you stick it out.

If you meet one like me, they will never commit any crimes.

A just person (as for justice) does not commit crimes.

I can be used as the bare minimum, a near miss.

You can just achieve something.

I'm the the height of action, the very definition of it.

Do

Or I can be how someone styles their hair.

A hairdo: do for short.

The ability to perform, so you are not going to quit.

It's the definition of the verb do.

With an e, and I become a female deer.

Doe a deer, a female deer (though technically in the song, they would be spelling it "do" as the note).

Neither male or female, I'm neutral as can be.

It is not gendered.

With an l, I'm cool and hot simultaneously.

Something that's lit is colloquially "cool" or could be on fire (hot).

Be wary though, I'm a frightening movie,

It is a movie based on the book by Stephen King about a clown that eats kids. (I think that's what he did anyway. I forget.)

Add a couple letters, and I move spontaneously.

Twitch is a spontaneous movement.

• Excellent job, you got it right. – Joe-You-Know Jul 13 '18 at 15:49
• It's a bit more complicated than just a clown eating kids, but +1 anyway :) – Mr Pie Jul 14 '18 at 3:12

I think you are

Do.

Add a letter to me, and you'll be thrown into medieval times,

Add the letter $\verb|v|$ to "do" and you can make "dov" which is short for Dover Castle.

Take one away and your stomach may be doing this.

Now take one away (namely, the letter $\verb|o|$) from "dov" and you are left with "dv" which stands for Dilatation Volvulus. I have not provided a link as to what that actually is, because it can be quite disturbing to read about (especially for dogs...) but it happens in the stomach.

Perhaps you could also let it stand for Daily Value, which is the percentage of nutrients in a type of food (because the nutrients travel toward your digestive system in your stomach).

If you meet one like me, they will never commit any crimes.

A word like "do" is "don't", and "don't" does not commit crimes.

I can be used as the bare minimum, a near miss.

The word "do" can be used as the bare minimum of a catch phrase during a near miss (metaphorically speaking). This is Homer Simpson's catch phrase, "doh!" in the TV series, The Simpsons.

I'm the height of action, the very definition of it.

Do means to carry out an action or some specific task.

Or I can be how someone styles their hair.

When you do someone's hair, it means you can style it (though that is Aussie slang for making someone's hair).

The ability to perform so you are not going to quit.

Described in the "height of action" line. But I think it is also a reference to Just Do It!.

With an e, and I become a female deer.

Add "e" to "do" and you get "doe", which is a female deer, even described in the lyric, "Do, a deer, a female deer..." (the "do" in the lyric is pronounced as "doe").

Neither male nor female, I'm neutral as can be.

Apart from how the word "do" has a similar sound to "dude", it does not have any other affiliation with genders.

With an I, I'm cool and hot simultaneously.

You can feel cool and hot on your wedding day before you have to say "I do" (note that the "I" has been added). Here are $5$ emotions that you might feel during your wedding day.

Be wary though, I'm a frightening movie.

Ok, this is a bit of a stretch, but I am going to go back to the "Just Do It" quote. The word "It" is a frightening movie (thank you Stephen King). You can check it out if you have not already seen it.

Add a couple letters, and I move spontaneously.

If you add the letters $\verb|f|$, $\verb|t|$ and $\verb|h|$ to "it", you can make the word "faith" and there is a famous quote, "faith can move mountains". Only problem is: it is three letters, and not a couple.

What am I?

Do.

Title:

Three words that will help you through your day.

...I now feel like the answer might be Just Do It... hhmmmm....