You should jump + Up b immediately afterwards, not release Up b. Optimally it would be jump and the frame after Up b. Up b completely cancels the jump animation. Release Up b is only faster if you PS and immediately afterwards press Up b. Moves only stale if you actually hit the opponent or an item, I don't think hitting shield refreshes your moves. As of with comboing Fair into Dtilt, it's not something I really recommend but it can sometimes work. It can work at lower percents if you hit the opponent with the Fair from close range. Comboing Fair into dash DB works in much more situations.
As of with Fair, try to mix up as much as you can so that they won't be able to predict you. Marth's Fair if spaced is pretty much unpunishable on block so they have to read what you'll do and reposition so that they can shield grab or anti-air you. Rising Fair is pretty good, but don't forget that to count the jump start-up too, it takes 6 frames before Marth goes into the air and then Fairs, which takes additional 5-6 frames to come out on grounded opponents. The thing with rising retreating Fair is that although the move itself is pretty much unpunishable if spaced right you're in the air afterwards above the opponent so you'll have to work on trying to land afterwards, which a good player won't let happen too easily. As of with FF and non-FF Fair, quickly landing with Fair reduces the shield advantage from the opponent, meaning that FFing gives them less frames to punish you. The amount of frames they can punish you are very little if you FF perfectly. However, a slow falled Fair has its advantages too. Because it takes longer before you land you have a chance to retreat even more or if hit them from closer range, even tricking the opponent with a cross-up afterwards is possible. Again you don't want the opponent to read you cause otherwise they can intercept you with their anti-air. but most anti-airs in the game are pretty laggy so you can bait and punish that too. There are so many ways to use the Fair and there is no best one, it depends on the situation and is heavily about mixing up those amazing options. As of with SH Fairs, how we move the control stick depends on how we want to Fair with it. There is no special way of moving the control stick to space it specifically as you want.
Where Marth wants to be? Having the opponent cornered. That's where Marth can shut down characters. But Marth definitely doesn't want to be cornered himself. While the opponent isn't cornered then yeah the center of the stage is best cause it's harder to be sent offstage there. Same with the air really. Marth wants to keep the opponent in the air at all time while he himself doesn't want to be above the opponent ever.
Offensively, Marth can use his disjointed moves to hit through plataforms. They can't air dodge through plataforms because air dodging makes you land on plataforms. The same thing with throwing out an aerial. Even if they shield it they're still on the plataform and have to shield drop to punish reliably, a thing which many people haven't mastered even today. You can also use plataforms to camp below them because the plataforms limits their aerial approach options. When Marth is the air, plataforms can be pretty harmful for Marth, or you can use it to trick an opponent by just falling through the plataform and just attacking them afterwards with something like Fair.