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....
