Can you get an edge in the market?
I prefer to think of it in terms of probabilities, and if you do your homework you can definitely increase your probability of success.
Is technical, fundamental analysis worth to study and learn about to improve your odds?
Is combining them going to improve your odds?
Depends on your time-frame and your approach to things in life. If you're daytrading, FA is not going to help much... probably not much help for commodities/futures trading either; but if you're trading stocks on medium to long-term time-frames, yes you must know FA, it will help you choose what to trade and whether you're willing to buy at a premium or a discount. Also, if you're the analytical type, it will help you build your conviction on what underlyings you're comfortable trading. TA can help you choosing when to enter and exit, but never do a trade based on TA alone. Learn tape reading, and understand what catalists will move a stock.
Does watching price movement on the screen for several years improve your profits and change you from a loser to a winner?
A DOM reader might say yes to that, personally I think having positions on the line, managing and taking the pain of cutting your losses, or the satisfaction of winning, will make you pay attention and learn your lessons.
Is randomwalk theory complete or are there exceptions in your oppinion?
I don't believe in EMT, bull markets have a bias to the upside and this will move the crappiest, valueless stock up given the right catalysts. The opposite is true for bear markets, the best companies will drop in price regardless of their valuation. In the end, all participants are humans and the markets in aggregate can behave in unpredictable ways, but for every transaction one side was right, and the other side was wrong. This means that to profit from the markets you must learn to trade both sides, long and short.