I looked into this too as I have about $15k in an old Scottrade account, and I would like to sell some stocks without paying commissions, but I haven't actually taken the plunge. I am not sure of all the details but I know that certain international stocks can't be transferred because Robin Hood only deals with US markets. I am not sure if it is possible to only transfer part of an account.
You are correct that dividends go into the funds available to be traded (my husband has an account).