Oh, yes. And it improves your game considerably when you identify the differences and learn to switch between the approaches deliberately.
Play the game the way you prefer to learn: switch between different experiences or concentrate on one game till you know the basics by heart.
But don’t try to emulate the more experimental and loose aggressive freeroll play at the cash table – it might work for some hands but soon enough the experienced players will start to raise you mercilessly and force you into difficult decisions.
You don’t want that, keep it as simple as possible at first.
I agree. Pot Odds, all the math involved, would be the perfect guide if only poker players weren’t such damn liars. 
However, they help you understand what the villain wants you to think what he holds in his hands. And they help you do the same.
Once you understand easily what they want you to think with the bet made, you will have a perfect starting point to identify all the hints that support or contradict this statement.
Also, the probabilities are more important in fixed limit when it’s difficult to get rid of other players early in the hand (because your bet limit is set) and therefore multiway hands are more commonly played and far more dangerous.
In pot or no limit the cards in your hand are far less important than your read of your opponents (and your ability to give a false impression in return).
True enough – of course, sometimes it’s quite useful to know the relationship between outs & odds.
Lets say you’ve hit the top pair (with a great kicker) or, better yet, hold a higher pocket pair than any card in the flop – but two cards on the board show a possible flush draw … well, then bet at least 2/3 of the pot, better yet, the pot.
If the villain has a draw and checks, he will be disappointed in around 64% of all these plays. Which means that you will make money in the long run against such players even if this hand is one of the other 36%. Because they bet more money than the odds give them in return (in the long run).
Some knowledge of outs and odds also helps you calculate the relative risk of speculative hands if you don’t know a thing about your opponent.
Lets compare two different hands:
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You have JJ in your pockets and the flop is 3Q7.
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You hold 97 and the flop is: AT8.
Both times 80$ are in the pot and the villain bets 20$ – what do you do if you don’t know anything at all about the other player?
Well, in (1) if the villain has the Q you need a J to win this, the probability that this happens is 8.4% (there are two J left, so the probability that you get one is 2/47 on the turn and 2/46 on the river).
Math tells you that you should fold the hand, so you should at least consider it.
But in (2) the chances for you to get a straight are around 18% and you have to pay less into the pot – so even if you think your opponent holds an ace, you should call his bet.
Of course, that’s the theory. In reality, what poker player would bet that low with top pair?
Everyone not totally stupid will always try to force you into a difficult decision and not a comfortable one – which is exactly what you should do in(1): Raise your opponent and let him think a bit.
More often than not, a raise or a fold is better than a check. You don’t learn anything at all with a check and encourage an aggressive stance against you.
Of course, a check has its merits: sometimes to hide your strength, sometimes to get a card for free, sometimes to bluff with a check-raise. But when you’re in doubt, a bet will give you information and the chance of a fold … which is nice.
Absolutely, you can’t stress that enough! You should have really mastered a level before you dip your toe into the next one – the water gets colder every time.
I’d suggest an even higher bankroll in no limit to give a relatively new player a wider margin when dealing with LAGs – who simply can’t be avoided: once everyone realizes that someone flinches away from aggressors with anything but the very best cards they will all fall on him and he will have a hard time to win at all.
Which brings me to one final advise (for now :D): make sure that the other players learn to respect your decisions!
Go to the showdown from time to time and show a hand that tells them you know what you’re doing.
Their respect improves every hand you play considerably and helps to fill your bankroll steadily.
I had three chances where I had suited high cards and the flop came with two more of the same suit. The river or the turn could have saved me with a flush but never did. Those three big bets were enough to see me on my way out of the game.