Should rich people give to the poor?

Yes, rich people should give to the poor. Even people who aren't rich, but have enough to spare should help out those in need.

they should pay taxes and give to charities if they feel like it.

absolutely. & so should people who typically aren't considered rich. by any historical standard, lower middle & middle class people are incredibly wealthy.
peter singer's essay on the moral obligation of rich people & rich countries to help the worst off has really influenced my thinking on this, & has very much changed the way i lead my life.

https://www.utilitarian.net/singer/by/199704--.htm

it seems to me a clear, logical truth that, if you have the ability to help someone who's suffereing, & you don't do anything, you're doing something wrong.

The problem is that the rich hoard money. They dont put it back into the economy, it just sits in accounts on and off shore. Poor people get money, they spend it. Perhaps, after they die a portion of their wealth should be redistributed into the economy.

Theres also all the tax loopholes to get rid of. At some point people/companies become so rich that giving them tax breaks, or incentive packages is just stupid. Give those tax breaks and incentive packages to the small business owners. Amazon doesnt need more tax relief.

With the deepest sincerity I must respond

https://www.youtube.com/watch?v=3B1IQYD4Uew

I don't think they should, but if they have money to spare, I don't know how they can sleep at night not doing so.

It would be nice if they did but the rich are under no obligation to give to the poor

Yes. I admit I am lower middle class and I still give to charities and even buy food at my local grocery store to put in the food pantry box in said store.