Playing 10-minute or other speed games is fun but teaches you very little. All the tips you are getting may help you be more successful at speed chess but if you wish to maximize your talents you will have to take the time and learn to analyze and calculate. See if you can play some longer time-controls to give you enough time to think your moves through. Thinking you have come up with the best move after several minutes of calculation and then having your opponent's move show you where you went wrong will teach you a lot about what factors you need to consider when analyzing a position. You won't learn as much when you and your opponent are both under time pressure and making the first move that "seems good".
Puzzles will demonstrate tactical themes, but the problem is that you know all puzzles have an immediate tactical solution, a condition that does not exist in 90% of the moves you must make in actual games. And don't try to learn a lot of specific opening variations--they won't help once your opponent makes a non-book move, and you won't really understand why lines are good or bad until you know more about chess. You would be better served by learning about endings--see the pieces' powers in the most basic settings.
There are a lot of books and lessons aimed at beginners. Some are mentioned here and looking at chess.com's Forum section "For Beginners" will lead you to many others. A great classic that explains the basics in easy-to-grasp language is "The Game of Chess" by Siegbert Tarrasch (be sure to get the algebraic edition).
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