Question 1 - Because your company told you--you might consider confirming your conversation with them in an email--that the RSUs actually vested and were sold same day for no gain/no loss, then go ahead and report it on your return. Report it as you suggested, that is cost basis equals sales proceeds for no gain/no loss.
Question 2 - Yes, because this involves just one trade (or even if it were a few trades) enter your information manually into TurboTax. Transactions of this type get entered in the Investments and Savings section of TurboTax online or in the Investment Income section of TurboTax CD/download.
Question 3 - Yes, given that the shares are not publicly traded on a US exchange, and no US broker was apparently involved in the transaction, report the sale as non-covered.
Question 4 - No, we assume you are a US citizen and therefore, you pay tax, if any, to the US Dept. of the Treasury. The US has various tax treaties with other countries that deal with issues where US citizens work for companies based in other countries. The situation might be different if you, as a US citizen, lived in a foreign country and worked for a foreign company.
Question 5 - No, it appears you have a very good understanding of what needs to be done from a tax perspective.
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