Ok, lets start off with one that is a little easier in terms of our using the inference and replacement rules to find out what method best suits you.
Here is proof #9 done in 6 steps;
Now you issue is how to attack problems like these.
The first method
you can use to attack a proof like this is to infer or replace all of the lines you are given to begin with. In the case of this problem, line #2 can be replaced via the exportation rule to make (R&Q)-->S. However, doing the problem this way is problematic because one you are done with that replacement, you are pretty much in the same boat because it does not give you any basic variables to break down the argument. When you want to attack a proof like this, it is always best to a) look for the most obvious inference rule, b)look for the most basic replacement rule. Keep an eye out for single variables, because those are perhaps the most helpful thing you can use in your proofs.
The second method
involves working from the conclusion forwards. You basically take the conclusion, in this case P-->S, and basically deconstruct it buy inversing the line. So for example, the only way you could get P-->S is by either Transposition or Implication. Transposition would give you ~P-->~S and Implication would give you~PvS. This helps out very well in simpler proofs, but not so well in this one. This way is really difficult though, so use this as a last resort.
Since we want to use the conditional proof, we have to indent and Assume (AP) P, the antecedent of the conditional in our conclusion. This is useful to us because it gives us a single variable which we can now use to make easier inferences with. At this point keep in mind, now that you have the P, you need to derive at some point in the proof an S because only then can you derive a conditional proof. Look at the proof. Where is there an S? When you become more familiar with the proofs, you can deconstruct as you form the proof from two separate ends. But for now, just try to deconstruct everything and form from the pieces you have.
We happen to have a use for out assumed premise. We can use modus ponens to derive Q&R. What we are essentially doing is trying to break down the proof into its constituent parts as much as possible. At this point, remember that you can break down a proof as much as you want and infer things that you may never use. Its wise to just break down everything to make sure you have a good inventory of inferences to use later on should you need it.
As we said, we want to break down the problem into the simplest constituent parts. So lines 5 and 6 are simplifications of line 4 so that we have more single variables
We see that one of the simplifications will help us derive Q-->S via modus ponens. At this point, notice how helpful it is now to just break down everything and then find out what stuff you can put together for your proof. It really helps out a lot.
From all of the fragments you have so far you can now see that you can derive via modus ponens S from lines 5 and 7. You now have all you need to form the conditional proof.
End the indentation and cite lines 3-8 where you started with P in line 3 and ended on line 8 with S, deriving via conditional proof P-->S.
So at this point, it may be helpful for you to tell me if any of these three methods are easy for you and if you prefer one to another. I can then elaborate some more on them and we can go through the other problems as well.