Patience, friend. This board is dead and moves slow, so I and potentially others don't check here very often.
Ftilt: Isn't Fsmash the better version with better range, stronger and similar endlag? When is a better situation to use this over Fsmash?
It got buffed at one point so there's differences now. You can basically assume faster startup and significantly better shield advantage than Fsmash. It also launches opponents at a lower angle, allowing for worse recovery angles and potentially earlier kills in some situations versus Fsmash's higher angles.
I'd say you want to use it versus aerial opponents (aerial opponents can fall out of Fsmash in some cases), when you want safer pokes on shield (hit with the tipper), and when you want to send them off the ledge at weird angles at lower percents.
Fsmash is more for ledge traps, reads, and punishing landings. It can work on shield in some situations if properly spaced, but I wouldn't recommend it. It's not really optimal for lower percents because it sends the opponent into the corner, where the blast zone is larger and that neuters its otherwise strong knockback. It's a pretty good kill option at the ledge around 80-100 though.
Dtilt: Can combo into lighting kick, is there any other usage to it? I know it's her fastest and safest hit out of her kit but its low reach, low damage makes it hard to use.
It can be a good shield pressure option as it is -10 and shifts her hurtbox low to avoid aerials. Combine it with the full charge of Phantom Knight to potentially combo into Phantom if they drop shield. You can also use it to 2-frame recoveries, which can often combo into kills under the right circumstances.
It also is one of her few boxing tools if you happen to get into an awkward point-blank scenario and it will be roughly as fast and safer than Nayru's Love or even Jab. You can even add it to strings when you are good enough and build some decent percent.
Dair: Besides edguarding people attempting to recover low, is there anything else? This move seems pretty bad overall.
It can stage spike into moves like Farore's Wind, Lightning Kick at mid percents, and Up-air at high percents. It is rather hard to land ordinarily with its high startup, but you can potentially kill early with the first two aforementioned moves and Up-air is pretty much a guaranteed kill at the percent it reliably combos.
Upsmash: Uptilt seems to be the better anti air and is also a combo starter. This is a finishing move but she seems to have better kill options then this.
This is legitimately a garbage move and is her weakest move in terms of versatility and relevance by far. I've only found it countering certain cross-ups on shield (Shulk Nair) and maybe some rare situations where you need its large amount of active frames to counter certain landing aerials (e.g. Bowser Bomb).
Down smash: I feel that Nayru's Love is a better "get off me" tool even though this is a little safer with better end lag. When should I use this?
Anytime you feel you can land it in a situation where you would otherwise use Nayru's Love. It offers far better follow-up potential and it will also send opponents at terrible recovery angles offstage. You can also use it at the ledge to 2-frame recoveries without hitboxs above them and opponents who regrab the ledge (losing invincibility). It is tricky to position just right to hit under the ledge, so you need to practice.
Upgrab: Sidegrabs is for stage control, Downgrab is for combo starter, what can this do?
Up-throw can kill opponents roughly in the 130% area. Use it when you are roughly in that percent range and aren't in a position to back-throw offstage. In rare circumstances, you might be able to mix up your opponent with the forward/back throws if they think you are going to throw them offstage, as the DI will not be optimal for up-throw and vice-versa.
Zelda's moves are optimized more for specific situations than they are for general use, so a little creativity is in order to maximize their strengths. Try experimenting against different characters and playstyles to see what works best for your particular style.