The RemoteDB works fine with load balancers, e.g., Amazon Load Balancer?
Not 100%. When a client opens transactions, RemoteDB keeps the transaction open in the server. This was built to allow migrating existing applications very easy.
If you don't use transactions at all, you could use a load balancer since RemoteDB would work in stateless mode, but I wouldn't recommend it anyway.
If you need high scale and load balancing, it's better to work with an architecture built for that, like TMS XData.