I believe so, but browser based makes it easier to run on any OS.
the browser version sometimes is hard to sync
OK, i have not had any issues with it, but the whole idea of supernodes is to allow you to run a lite wallet on your device and connect to a node on the network.
This will be a huge step forward.
is the lite wallet secure to use?
Obviously you need to trust the server you're connecting to since it's watching the chain for you and could theretically lie to you about it's contents. So while it could not steal any of your funds it would theretically be able to trick you into think e.g. a tx is there when it really isn't.
To be clear: This is not a specific problem with NEM. In any blockchain if you're not keeping track of it yourself you have to trust the party that does this for you.