No, this is completely wrong. Filing has nothing to do with "having some financial ties with the US", it has to do with being a US citizen. You are double taxes with some extra write-offs [1]. The 10 year thing comes if you give up your citizenship for tax purposes (if you have over $2million in assets this is automatically assumed). In that case you are taxed at a higher rate for 10 years before finally getting off the hook. If you give up your citizen for other reasons then you only have to file for one additional year.

Oh yea, if you have $10k at any moment in the course of the year you must report all bank accounts where the money was (i.e. 3k in one account, 5k in another, 2k in a third, report all 3). You wont hear about this rule unless you live in a so-called "tax haven". Guess why that is.

[1] This is very complex. For a single earner you can take an exemption on the first ~$80k. In most of the US that's a lot of money. Not necessarily everywhere, so depending on where you live you may hit this pretty fast. Taking the exemption makes you unable to claim certain things so you can also chose not to take the exception and use a more complex form. I have a tax guy do this for me (takes him over 3 hours to go through the paper work) and costs about $1k/year.

Only if you give it up for tax purposes.