Newbie/Noob here, Help!

First of all, dont play by the rules! Im not asking you to cheat - never do that! - Im telling you to forget the common sniper rules. If you play by the rules of common snipers, you are dead in no time. These rules are well known and I rather ask you to think ahead and in advance.

When you ask yourself "What would a sniper do?", then DO NOT DO IT!. Every "Depp" (google it!) and his mother knows this behaviour of common snipers and hence: Sniper dead!
Think beside the common rules and the win is yours again.

2nd rule: Dont cross my way, my bullet is faster than yours

I'm surprised nobody has said this yet, but what you're seeing here is an effect of latency and clientside hit detection. Allow me to explain.
Hits in this game are calculated locally, on the shooter's machine. This means that the world state on the shooter's machine is what
"matters". If you can see someone and hit them, it counts.
However, this is a networked game, so not everything is perfectly in-sync. On the victim's (player 2's) machine, your (the shooter) avatar is a few hundred milliseconds behind your actual position. When you start shooting player 2, they don't receive hit indicators until a few hundred milliseconds after you started shooting them.
TTK in Planetside is rather slow. Since hits are calculated in realtime when you're the one shooting, you experience the full TTK (9 or more bullets, like you said). Player 2, however, due to the initial latency, experiences a much shorter apparent TTK (feels like 2-4 bullets) before they're killed, even though you actually shot at them for the 'full' TTK duration.
This, of course, is also true in reverse. If player 2 shoots at you, it will appear to take a lot longer to kill you on their machine, and a lot shorter for them to kill you on your machine.

The solution to this is to take cover IMMEDIATELY after receiving hit indicators. Once you start taking damage, you must realize that the shooter has already been shooting you for a half a second or more, and you could already be nearly dead. That damage won't appear on your end for a few hundred milliseconds, though (explaining why you can continue to apparently take damage after you've ducked behind cover.) Furthermore, because of latency, when you duck behind cover, your avatar on Player 2's computer won't do so for another half a second or so. During that time, thanks to client-side hit detection, they can still 'legally' shoot you, even though you're already behind cover on your screen. All of these things add up to why you must immediately seek cover when you start taking damage (unless you're taking damage from the target you're currently engaged with, and you're confident you can kill that target before they kill you.)

Anyway, I made a video gameplay of mine:


Wondering what I did wrong that I died so much

I'm not the best for advice but a couple things I noticed that lead to you dying a lot is that you weren't moving around very much during engagements which lead to you getting headshot and that you kind of tunnel visioned, as in you weren't very aware of your surroundings. At about 7 mins in you were looking down towards the teleporter when you were flanked by an infiltrator after he killed a few of your nearby allies. If you had listened and looked at the mini-map you would've been able to turn around and likely kill him while he was preoccupied with the other people.

I took a look at your Video and although it is fairly short, there are some Things that I can say about it:
1. You engaged a heavy with an active overshield, wich means you Need to drain his overshield first, that would take about 4-6 hits i think. Then you would Need to drain his normal shield also 4-5 hits, then you would Need to kill his life, while he is probalby using nanoweave armor and making bodyshots only you Need 6-7 bullets.So you actually Need half a mag to kill a heavy assault. (whithout any headshots.)
2. He hit you with his rocket launcher directly, which is an instant kill.
3. You sprayed all over the place, this should only be a Panic Option, take your time to aim, go for the head make short burst, no more than 5-10 bullets (which actually is a large number, most would suggest even Shorter Bursts.)
I personally don't like the lasersight, i'd take Forward grip on any weapon anytime over it.
4. Try to predict the movement of your target and aim ahead, even at short distances you will miss a lot of shots if you don't.
5. Running up straight to a window is generally a bad idea, you engage coming out of sprint, that puts you at another disadvantage.