Whatever we see is basically based on the light that hits our eyes, right? When we look at the Moon we are looking at the Moon as it was couple of seconds ago, as the light takes some seconds (~2 seconds I believe) to reach us. In a way aren't we ALWAYS seeing the past as, no matter how close we are to something, we can never be at distance 0. Am I wrong in thinking about it like that?
That is technically correct. Since the speed of light is finite, it takes time for light from any object in the universe to reach us, even the Moon which is fairly close. For things on Earth, the distances involved are very small compared to the speed of light and so we effectively see thing "instantly".
The moon is about 1.2 light seconds away so we're seeing the surface of the moon as it was 1.2 seconds ago, still effectively instantly.
The sun in about 8.3 light minutes away and things get further away and more distant in time as you go out.
You are correct. For every foot (~30 cm) away something is, you're looking back a nanosecond.
Well, the "standard" answer is the one given below (that's why we use telescopes to look at the past universe). However, I'd like to qualify this.
The Einstein twin paradox (time contraction) implies the following thought experiment: With a very good telescope, you look at a planet 10 light-years away. And there you see an ET entering his spaceship and flying to earth very fast (but not as fast as light). 4 minutes later, the space ship lands near you, and the ET comes to you. You say "How long did you travel?" and the ET says: "5 days (of planet earth)".
Weren't you suppose to look in your telescope at events which happened 10 years ago? For you, for the ET, all happened in a very short time (compared to 10 years). Only if the ET goes back will he find its planet 20 years older (and he will only be 2*5=10 days older).
So we have to be careful when saying that we see the past. Because this past could suddenly become present ...
For those who doubt that, I will use the example of Wikipedia: Twin Paradox.
A space ship on earth goes and come back to a planet 4 light years away, at the speed v=0.8c. During its travel, it sends (at the speed of light) a movie of its clock to earth (this is similar to looking at it in a super-telescope).
We are only interested at what happens on earth.
For the space ship to go to destination, a clock on earth counts 9 years, and the clock in the movie from the space ship counts 3 years. On earth, a local clock moves 3 times faster than the clock in the movie. For the space ship to return, a clock on earth counts 1 year, and the clock in the movie from the space ship counts 3 years. On earth, a local clock moves 3 times slower than the clock in the movie.
The total travel time is 9+1=10 years for a clock on earth, and 3+3=6 years for the clock in the space ship (or in the video, or looked at with a telescope).
If we only consider the return part of the travel, the space ship is seen (with the video or in a telescope) starting from the planet located 4 light-years away and arriving 1 year later for the clock on earth. The clock in the video says that the travel lasted 3 years.
The values in my first example are for a planet 10 light years away, and a speed $v=(1-$10^(-8)$)c$.
For a planet 1 million light years away, and a speed $v=(1-$10^(-12)$)c$, the space ship arrives on earth in about 30s, and the ET says his travel lasted 1 year and 5 months...