1. I have never had a saltwater tank, but I would be surprised if a light/moderate brackish setup like you are talking about would be able to keep the live rock, well, alive. Probably would have to ask a true saltwater expert about that. If the brackish water isn't salty enough to keep the live rock alive, then it's not going to help your cycle any as all the organisms in there will simply die.
2. There is no reason you couldn't cycle a brackish tank like you would a freshwater tank.
3. Another option, and one that might be the best of all given what you say you want to do, is cycle the tank as a completely freshwater tank. Then add your mollies & ghost shrimp, and then slowly (over the course of a month or so) transition the tank from being full freshwater to being brackish. I say this is perhaps the best option because, let's face it, most pet stores keep their mollies and their ghost shrimp in pure fresh water. If that's the case with your pet store, then it's not like you can simply bring them home and then plop them down into a brackish tank...you'll probably kill everything almost instantly. So you're going to need to do a long-term acclimation anyways, why not just do it in your main tank then? As long as you do it slowly enough (like I said, over the course of about a month or so) your filter bacteria will be able to adapt so you won't have to re-cycle the tank. I've done this before, so I know that's the case. And I did it in a tank with ghost shrimp, so I know that freshwater ghost shrimp can be acclimated to moderately brackish water successfully as long as it is done slowly.
4. HoB filter is fine for a 20L. The only thing to consider is that you should either have it hanging somewhere near the middle of the tank; or if you don't, consider putting a small airstone or something at the opposite end from where you have your filter, just to help keep all the water circulating in the tank. Since 20L's are, well, quite long, I found that if the HoB filter is at the far end of one side of the tank, sometimes the amount of water circulation at the opposite end is really quite minimal (to non-existent), depending upon the arrangement of "stuff" in the tank. And you never really want to have "dead pockets" develop, so a simple air stone can be a solution. Or if you don't like the idea of an airstone in the tank, you could be creative with the outflow of the HoB and use a piece of driftwood or something to help "direct" the flow in the direction of the rest of the tank so as to encourage water circulation.
EDIT: Regarding #4, it may end up not being an issue. I had in my mind a 30 long, not a 20 long. A 20 long might still be short enough that an HoB at one end will create circulation throughout the tank. But if it doesn't, then just consider what I said in #4 above.
