pixel made a lot of very good suggestions
emo_prinny...watching your own character isn't the best thing, you should be watching your opponent, watch what they are doing, look for visual cues to their next move, there are a lot of moves that you can visually see coming
overall suggestions...
learn the defensive properties of the game as a whole, spacing, blocking, throw breaks, GI, stun break, air control, wake up, etc are all very important parts of the game and the longer you can survive the more damage you can do.
Learn basic gameplay mechanics...
above covers alot of these things but if you find something mentioned that you dont understand ask how to do it and practice i.e to practice throw breaks record throws against you than practice breaking them, this wont help the mind game any but it will help you understand the timing of a throw break
if you don't know what a game play mechanic is or even what that means....where do i start...ask...the newbie silencer answers can help identify things you don't understand or know about...again ask questions
all the above stuff can be done by yourself, SC4 lacks a tutorial mode like VF4Evo but if you go over and root out all the different game mechanics you can find ways to practice them with recording mode.
execution is extremely important, if you have the confidence that you can execute properly it will improve your overall play because you don't have to think about doing a move, instead you can focus on when to do the move
i would recommend
1 learning all of your characters signature moves
2 set the cpu in training mode to hard and practice the sig moves
and learn what can combo from them
3 dont forget to use the up and down movement
these are the things that have been working for me. im also new too SC4 however i do play other fighting games (VF5 ,king of fighters) also play people that are better than you and watch how they move thier characters around your attacks
i disagree with your recommendations, they aren't wrong, they just aren't very complete. why?
learn a character's entire movelist, the signature moves don't amount to a drop of water in a bucket. practice is good,
practice everything...again execution is extremely important, practice for precision.
setting the training dummy to hard is fine, i haven't used the computer active training dummies so i can't comment on the quality of play. all the stuff i mentioned about recording and making your own practice sessions applies here.
if by "up and down movement" you mean 8wayrun than yes. practice moving in all directions...the 8wayrun system is a signature part of the SC series. it allows 8 directional movement and has an entire attack system and mix-up/mindgame based on 8wayrun. its very important to understand how you can move and what you can do while moving...again practice the entire move list this will give you and idea of what options are available