With shape of the earth, I see some of this from the skeptics but rarely from the round earth side.

Science just learns from history, and the flat-or-round discussion already took place hundreds of years ago.

I don't get what that means. Or why you're comparing "flat earth" to "science".

In this instance I meant mainly astrophysics and modern physics for "science" here.

When I go outside and look around, I see flat.

I don't.

I see a horizon where everything disappears, which would not be possible on a flat earth.

I see a lot of pictures showing "things you shouldn't see on a globe earth", but in those cases the publishers forgot about refraction, and still magically the bottom of structures shown is hidden behind the curve(which somehow is always ignored by flat earthers).

Distance to the sun seems hard to measure accurately.

The public is never able to do any accurate measurement, but that doesn't matter. What matters is that there will be a very different result than what some flat earthers believe:

The sun is not in the upper atmosphere.

Earth's rotation? What do you mean? You've actually observed it rotating?

I didn't, but a bunch of flat earthers did with a ring laser gyroscope. :D

You could also build a foucault pendulum for that.

Radius.. did you drill a hole and go to the center?

You would just need to measure the sun's relative position at two different points on earth at the same time. It's that easy.

I don't see the satellites.

Then go out of your light-polluted city and observe the sky for some time.

Also yes it would prove round earth, as the satellites would fall straight onto the ground due to gravity in flat earth.

I never saw someone from NASA at my school

Here I just wanted to point out that it's not only NASA, but several other institutions, like those in europe, russia, china, …

Also NASA is not the founder of round earth, but does something very different: Space exploration.

Trusting what other people tell you might be a reasonable choice. Trusting what other people tell you is a fact of life and if we never did it we'd never get anywhere. But it's not science is the point.

Well anyone who wants to challenge globe earth can do that. He would just need to repeat a bunch of ancient experiments.

I can easily judge that you don't seem like a bot

What if I said that two of my answers in this comment are actually the answers of a chat bot?

Can you identify them?