I'm a US citizen who has lived in a few different countries (UK, Taiwan, China, now Canada). Sometimes, I have kept a US address on my accounts (when I anticipated returning to the US) but now I mostly have Canadian addresses on them.
In answer to your specific questions:
1) As of today, Fidelity will allow you to keep (and trade freely in) retirement accounts, but not non-retirement accounts. Many other US brokerages are similar to this. Vanguard is actually one of the least friendly to expats -- you can't even trade in a retirement account with them.
2) If you want to move your funds to another brokerage, the advice above about doing it as an "in kind" transfer is good -- that means it won't be taxable. I did this to move stuff from Vanguard. What I did was first convert my Vanguard mutual funds to the equivalent ETFs (a non-taxable event) and then transfer those ETFs in kind to my new brokerage (a non-taxable event). It took some time, but it was pretty straightforward, free, and didn't require paying any taxes.
In terms of general advice:
- I would recommend opening accounts at expat friendly US brokerages (e.g. Schwab) BEFORE you move. Even the friendly ones don't necessarily like you opening an account from overseas.
- Interactive Brokers could be good, but they're not useful from Canada so I don't have any experience with them.
- For a taxable account, the easiest solution for me was to move my US ETFs to a Canadian brokerage. I didn't sell anything, and they're still in USD. My brokerage gives me tax docs for both the US system and the Canadian system, which is nice. Depending on the country, though, this might not be doable.
- Understand tax treaties BEFORE you move. For example, which retirement accounts are recognized by which countries? Are there any steps you need to take to get them recognized? For example, Canada does recognize Roth IRAs (which is great) but you need to file an election with the CRA (Canada's IRS) in your first year of residency.
- Personally, I've kept accounts open at a bunch of brokerages. You hear horror stories about folks being told by a brokerage that they have 60 days to vacate the premises, so I want to have options. I'd love to simplify, but because policies are always changing, I have my accounts spread around.