You just need to get a better grasp on when using context is enough and when it isn't.
Quoting from your examples:
"There isn't much we can do unless you tell us why you were there." The cop tells the woman.
The woman nervously taps her fingers on her arms and answers her question.
Here context is not enough. Apart from "her" being repeated, you'...
If you are trying to minimize the number of words, it will help a lot if you stick to the old rule, Show, don't tell — Wikipedia (a good rule to follow even if you aren't trying to save words).
Telling the reader about something requires words. But showing can be incorporated into the plot.
As the hover-car approached the massive Ministry ...
Going out on a limb a bit here, but I feel like "I" in a first person (non-dialog) narrative is redundant in a way. It's already first person, so "I" doesn't really add anything of value. I wouldn't say it's inherently bad, but an alternative is almost always better.
In real life we only really think of ourselves in terms of "I" when we are actively ...
2000 words is a tight constraint indeed. While you can show something in that limit, you can't show everything that you mentioned in your question.
Sci-fiction is famous for having a lot of short stories authors (I think of Asimov, of course, but I'd suggest to take a look at Ted Chiang's "Stories of your life" too). Even then, 2000 words ...
It's not particularly difficult. Tense is a tool feared by too many aspiring writers.
What you appear to be asking can be seen in Forrest Gump (film).
I am sitting on a bench waiting for a bus (present). Whilst I'm waiting I will relay to anybody who wishes to listen events that led me to this point in my life (still present).
My momma was . . . (past).
Is "my" and "me" prohibited?
I stood up and began to walk across the room. She turned away at my approach.
My urge was to comfort her. Standing up and walking across the room, she turned away from me.
Other than that, I'd say buy a book and read the guy.
Usually "and" is indeed dispensable and the fact that you wrote it is a clue to check if it is. Using that sentence as an example, I can eliminate "and" with a semicolon, or a period.
Usually "and" is indeed dispensable; the fact that you wrote it is a clue to check if it is.
Usually "and" is indeed dispensable. The fact that you wrote it is a clue ...
I agree with Surtsey's answer: one thing are stylistic choices and characterization, another is fixing mistakes during a revision.
If the problem is "i tend to overwrite", the only solution will be passing the novel through another revision where you specifically take care of this aspect, cutting down unnecessary words, simplyfing sentences, synthetizing ...
The simplest answer would be to try writing it like you're telling it to someone. You could use a "rubber duck" method to test it out: Place a rubber duck (or something similar) next to your computer or wherever you write, pretend it's a person, and try to explain the manuscript to it from your point of view. Make sure to insert your personal reactions/...
It can often help to clearly separate who you're talking about. If you have different genders in conversation, it's easier, but you'll just have to find another separator for other situations. Like this:
Woman_1 said something.
Woman_2 thought about it, tapped her fingers and the side of her arm, and answered.
"But it's not like this, it's like ...
Personnally I organize my writing in this way :
"I'm against this ! told John, protesting vividly. He stood up from his seat.
- You cannot stop us from taking this decision !" replied Steve. He stood up too.
Afterwards, you can continue to use "he/his" if you continue to talk about Steve. Otherwise you need to specify that John is doing something.