Scenarios: You send $10,000 to a foreign country's savings account. You earn $100 in interest and report it in your individual income tax return. Later, you send $10,000 back to the US and gain $50 due to a change in exchange rate.
In this case, do you have to report $50 you made due to exchange rate change in your individual income tax return?

Yes, see Code § 61 ("all income from whatever source derived"). The $200 de minimis exception in Code § 988(e)(2) would not apply because this would not be a "personal transaction." Code § 988(e)(3).

Yes, you would report it as a capital gain.

The duration of the transactions being longer or shorter than a year and a day would determine whether the gain is long-term or short-term.

The gain would be ordinary income. See Code § 988(a)(1)(A).

That seems counter-intuitive, but I yield to your greater expertise.