Hi Edmond... welcome to RCBuddies.com. Glad you could join us here.
I'll try to answer your questions to my best ability but no guarantees I am 100% rite haha.
To your first paragraph's comment, I noticed you mentioned that your blades are also wrecked a bit at the edge. One thing you should know is that for RC Helicopter, due to the high spinning of the main rotor blades and the load it generates, any little damage to the blades should always mean that it should be changed immediately. Do not try to fly the helicopter with damaged blades. It can be very very dangerous and it is not worth saving the money on something critical like that. So please go change the blades. This applies for both Main Rotors and Tail Rotors.
For your first paragraph, I can only imagine that the damaged blades has something to do with the nodding of your helicopter. Change the blades and see if it still nods. While changing the blades, please also check the shaft to ensure it is not bent. Basically your helicopter needs to be able to spool up or spin without any "vibrations". Tails shaking up and down (resulting in a nodding effect) can also be due to a variety of factors like low rpms. You might want to try increasing your headspeed a little up or maybe sometimes even down. Are your tail blades damaged ? Is your tail blades and belt turning over smoothly?
If you find that your shaft is bent then you will need to replace the shaft and you can also perhaps replace the main headblock to alluminium. Its always better and more precise with alluminium headblocks plus it looks cool

Don't change it if you don't have to because as a beginner, there will indeed be quite a few crashes. It's unavoidable. You need not waste money here unless you want to. Basically alluminium is better than plastic but it is also costlier.
As for the simulator, if you already have the controller, then you should just use the controller unless you fear damaging it. I personally have a spare controller which I use for my sims. I have two because the one I use for my Sim is lighter than the one I use for my real flying. Apart from that, there's no reason why you need two separate controllers. As with all things, the more you use it... the faster it breaks down. But for it to breakdown, I would think you will need to use it A LOT before that happens. Go buy the cable and buy the sim and you'll save a lot of money when it comes to learning without having to pay for spare parts. I bought the original sim at RM800 or so (can't remember) and it has paid for itself many times over already.
Good Luck and Happy Flights!