"1) Do we have to report income on Brokerage accounts only within US or any brokerage account outside the US?"
Your United States income tax return is based on your world-wide income. Ergo, income in brokerage accounts outside the US is reported.
"2) Let's assume I started my account with $1000 and ended up with $1500 by the end of the year, which means I have to pay tax on $500 earned."
Your statement leaves out too much detail. If the +$500 is unrealized gain, (the value of the security went up but you didn't sell), then you have nothing to report. If the +$500 is a realized gain, (the value of the security went up and you sold), then you have reportable income. If the +$500 is due to reportable distributions of your securities - dividends and interest - then you have $500 of reportable income. And, of course, the +$500 could be some mixture of unrealized gain, realized gain and reportable distributions in which case your reportable income will be >$0 and <$500.
"What about next year? Should I take my base/initial money as $1500 and calculate my taxes on profit above $1500?"
Maybe, maybe not. It depends entirely on how that $500 originated as described above and on the composition of "next year's" increase.
"3) How sensitive is IRS towards details? I am sure we may miss certain small amounts when dealing with hundreds of trades within a year. "
You'd really have to ask the IRS that question. But if you're doing hundreds of trades a year through US brokerages the IRS is going to have all of that detail reported to them.
"4) An off-side question: I remember opening an account with a couple of brokerage accounts, but have never traded with them, never deposited money into them. Do I have to report those accounts on yearly filings to IRS? What if it was just a demo account that I opened, does it count as an account that has to be reported to IRS?"
If you have no real activity in the accounts you have nothing to report.
As an "investor" and as a person subject to US taxes it's actually your responsibility to keep track of your world-wideinvesting activities.
