Heeeeya there, welcome to the community!
Ok looking at your stats you've had a fairly typical rough-start-for-a-newbie thing going, it can be frustrating but don't worry and push on (like everyone here did)
Your PC specs are excellent, 3770K + GTX670 is more than enough for C2. Obviously you don't want to be attempting DX11 Ultra + High Res textures in multiplayer, it will only kill framerates on pointless details...so set the graphics to whatever lets you stay ABOVE 60 fps at all times and you'll be set in that department.
Now for playing the actual game...I'll try to address your concerns:
- You did land some (or most) of your bullets but the killcam from a first-person perspective will still make it look like your bullets are going off the edge of the screen and "missing". Don't worry, they are not.
- Kill replays make no sense and/or are extremely delayed. This is simply how the C2 Killcam is, there is no helping it. This is why you only use the killcam to get an idea of the location of your killer and the circumstances under which you were killed - don't bother going by a bullet-by-bullet basis because most of the time it will make no sense. It can also be used to determine hackers, though since you're new it can be tough to differentiate between a hacker and a good player.
- When someone shoots you, you die 5 seconds after they stopped shooting? 5 seconds?? That can't be right...either something else killed you, or the server is completely lagged-out (quite common, it's a buggy game). Often stuff like Orbital Strike can lag out the whole server which makes everyone freeze in place as far as the server is concerned but they're actually still running around, so when the server "unfreezes" you'll see a whole lot of random deaths and...yeah, it's pretty stupid. Nothing will be done about it. I think that's what you experienced.
- Spawn-kills - 9 out of 10 times the game will try to spawn you away from enemies and it does this quite well. Sometimes if an enemy player has managed to come all the way to your side of the map on his own (all other enemies are still on the other side), yeah you'll end up spawning nearby him and could be a free kill. It can also happen on really small maps like Impact when there are lots of players. But this is fairly rare compared to the kind of spawn rubbish you see in Call Of Duty. You could also be experiencing the server lag glitch as described above, which results in a whole bunch of players dying instantly upon spawn.
Firstly you need to make sure you are on a server which is geographically close to you, i.e. gives you a good latency - standard stuff as with any online game, if you play with lag you're gonna get screwed. On the far right hand side in server browser (and scoreboard) is a latency indicator. It is crude and inaccurate, but it will still give you a good IDEA as to whether you are in the green or lagging like hell. Here's how I see it:
<50ms = excellent
<100ms = great
<150ms = playable
<200ms = borderline playable
<250ms = punishing if you make mistakes
<300ms = you'll start seeing weird things happening
<400ms = don't bother
Also re-bind stuff like Visor and Nanovision to keys (or mouse buttons) which you can easily reach, the default setup binds them to B and N respectively which are awkward to press in heated battle
So now that you've got smooth framerates and only go on servers which give a decent ping, I'll leave you with this guide which will take you through the Nanosuit modules and gameplay tips in MasterJedi's sixy accent...
And of course something from SDub, a lovely series called "Tactical Tuesday" full of lessons/tips and gameplay footage, take heed to his words...
http://www.youtube.com/playlist?list=PLJ94-fHMfAt1b0pHKmEG5v20lyAIa5Wwf
The above videos could potentially save you 100+ hours (maybe even more) of having to learn that stuff the hard way ingame, but remember in the end it boils down to practice.
Good luck!