9x servo on Arduino Nano?
I'm afraid that with PWM controler I won't be able to do that.


Chances are that any PWM controller is going to let you control each output independently. 

According the the servo library documentation, the library can handle up to 12 servos on a single Arduino, so your project should be feasible. It will however reduce the number of PWM pins available from 6 down to 4.


  Will a 9V battery power all these servos?


No! Not a chance.

Typical 9g servos consume 150 mA without any load, and stall at ~700-900 mA. A typical 9v has ~500 mAh capacity, and most data sheets show loads of ~100-150 mA max. Your 9v might be able to supply a few amps for a few seconds before they heat up and slow down.

If your load is very light 9 servos will consume ~900 mA; an ideal 9v would last at most 30 min with this load, but real batteries aren't ideal and will heat up and loose efficiency. 

Near maximum load your 9 servos will draw ~7000-9000 mA, well beyond the capabilities of a 9v. However those numbers are for 5v so you could cut them all in half.

If you used an appropriate 5v step-down DC-DC supply you might be able to power all 9 servos for a few seconds before the batter overheats and gives up.

If you powered them directly, the servos will have to dissipate more heat, and will draw extra power, could damage the servos if the batter could supply enough juice.