Get +12/-12VDC out of 24VDC Supply

Your switching supply output is isolated from the input via it's transformer. It also has a plastic case which should have a double insulted symbol on it somewhere (two squares, one within the other) This means the output is "floating" (i.e. not referenced to earth)

Never tie the mains neutral to earth, they both serve very different purposes. Although they are actually tied together at the house's input (in most house wiring systems), the neutral is for return currents and the protective earth is for detecting fault currents and keeping (metal) equipment cases at a safe potential.

You sometimes see plastic cased switching supplies with an earth lead, which is usually used for the EMI filter and to reference the output to earth. Sometimes tiny leakage currents through the transformer windings (or the EMI Y caps if the earth is left unconnected) can charge up the output (relative to earth) to a reasonably high voltage, enough to give you an annoying (but safe) zap when you touch one of the terminals. The earth can be used to drain the leakage currents.

So you can tie the isolated output to earth if you wish, but just use the L and N connections as directed on the mains side.

Further reading:

Safety Considerations in Power Supply Design
Power Supply Technical Guide - also deals with other aspects unrelated to the question, but very thorough and detailed.
UL1310 - Class 2 Power Units
UL1012 - Power Units Other Than Class 2

First: Can i possibly eliminate this kind of noise when it comes to a switching supply for audio, maybe with a better filter or something with simple components, or do i have to go running back to the old transformer+linear regulator for this kind of application? (which i really don't want to do)

Well I may have missed what your initial source of the 6-12V is. But regarding the higher voltage supply, NO... you don't have to go back to a brute force supply. The noise can be eliminated or at least minimized. But I've dealt with this kind of thing quite often, and here's what you're in for.

1. the fact that you're hearing frequencies well below your original oscillator frequency of 70Khz does indeed point to parasitic oscillations. The bad news there is that there may be points of instability in your high gain circuit that will "ring" for a short duration at 400kHz every time a strong "impulse" signal is applied. So if "hash" noise pulses from your 70khz is continually supplying the impulses through the supply lines, the "triggered" parasitic will always be there. The bad news there is that you could find that even with the two isolated supplies, certain music signal conditions could still cause those same parasitics to rear their ugly head.

2. It is still possible that the 400khz or other parasitic frequencies are being generated within your booster circuit. They may be very small so you don't see them on the scope, but you did say you were dealing with a high gain circuit. I recently worked with a pre-made variable "boost regulator" whose internal oscillator was around 170khz, and still got horrendous "hashing noise" (more like white noise then a single tone" in my target circuit.). But the principals of propagation of the noise don't change. They are basically electric, propagated through the power supply wires themselves, and magnetic, propagating through the air, and radiating from the power supply wires. If your target circuit has ANY inductors, that radiation can be a major nuisance. To reduce it, you can start by adding a PI filter to the output of your switching supply, consisting of a shunt capacitor followed by a series inductor, and then another shunt capacitor. If the supply wires feeding the 555 circuit are of any length you may need to add an inductor there too. The capacitors should be the fast and low ESR kind, such as polypropylene metalized film. Its hard to pinpoint the perfect values, and even when you do they almost always need to be further tweaked. But a good starting point would be 100uH for the series inductor, and 1uF for the caps. That should at least audibly reduce both the electric and magnetic sources. However, if magnetic field transference is indeed part of the problem, you may have to go the extra steps of making the supply lines into a twisted pair, keeping them well away from any inductors in your audio circuit, and in some cases increasing the distance between your 555 based power supply and the audio circuit. Finally, while most IC manufacturers push for the very fastest switching possible in their ICs, you might lose some headaches in this case by going to a slower version of the 555. If it has a slew rate capable of building an oscillator in the multi-megahertz range, then those edges can cause you problems even with a slower clock speed.

Oh and by the way, here's a little known trick... if you place an ordinary silicon diode in your 555 oscillator circuit, such that the anode connects to pin 7 and the cathode to pin 6, you'll be able to get to a nearly perfect 50% duty cycle with both R1 and R2 the same value! I don't know why this trick is so seldom published, but it works. You can then play with different switching frequencies by just changing the timing capacitor.

Now for this part...

Second: When it comes to a using this kind of devices on stage, usually there are a lot of sources from noise (electromagnetic, ground loops, etc..). Is a Transformer+Regulator more or less immune to this kind of noise than a switching supply? Please explain

It really won't make much difference, if any. If you get to a quiet situation with your current supply setup, and the physical setup doesn't change on stage, any additional noise you get at performance time will likely be due to another source. At performance venues there are a whole slew of issues, and the biggest one related to power supplies is "ground loops". These occur when the power supplies of two or more separate pieces of equipment somehow allow small amounts of 50/60Hz AC to reach their "ground" points. If the equipment is then plugged into different AC sources that are even a few volts different, the ground shield in any connecting cables conducts the AC from one device to the other, coupling the "hum" right into your audio stream. To avoid contributing to this problem, its more important to understand the leakage between your AC source, through your power supply components, that can end up coupled to what you HOPED would be ground. isolation is key. You'd never want to use a supply circuit that didn't have transformer isolation somewhere before you got to the AC mains. And it never hurts to plug as much equipment as possible into the same power strip, fed from a single AC source.

And then of course there is radiated electromagnetic noise. Are you performing anywhere near a 10,000 volt neon sign? Pickup from that kind of noise can't be helped by your power supply. Only adequate shielding, and in some cases "nulling" techniques (such as hum-bucking pickups) can help you out of that headache.

Good luck man!