Thanks mate. So essentially, there's interoperability between SegWit and legacy addresses, so there should be no issue transferring coins from an one to the other (including sweeping, which is just a method of on-chain transfer), right? If I had coins on a SegWit address and wanted to sell, I could just transfer them to an exchange if it it hadn't implemented SegWit yet?
Exactly, yes.
Segwit is backwards compatible (except Bech32 segwit addresses but that's because it's a new address format) so you can send and receive from Segwit addresses.
The thing on opensource is I'm not a coder, so I have no ability to evaluate if the either of the services listed in point 1 are legit or sketchy. I'm really relying on other people with the expertise to know there.
Use popular ones that are open source then.
That way the more people that use it the better chance it is scrutinized properly by various people with different experience.
Coinb.in is popular, old-ish and open source so it's good, but you'll have to download the website on a live CD on an airgapped PC to use it safely.
Why not use Electrum instead?