Assalam o Alaikum brother.
Considering what you are saying (brake pedal presses down deep before you feel brakes working), I would recommend you to get your car's brake fluid checked. According to my information, the pedal goes down deep mainly when your brake system is low on brake fliud. Get it checked from a good mechanic.
Secondly, if your brake disk (tawa called by some local mechanics) or prake pads (leather called by some local mechanics) are worn out, I'd recommend you to get new front pads and disks from Honda not other kinds.
I had an issue with my city's brakes too. The problem was that when I used to apply brakes, strong vibrations were felt in brake pedal and in steering wheel with a really disturbing sound. The pedal tried returning back. I could feel the pressure the pedal used to apply back to my foot. It was a struggle keeping the pedal down. My father got the car checked from a mechanic and he advised to get new brake disks (from bilal gunj). He said the brake disks have worn out completely (he also said the not even tooling will help which I think he asked you to get done from khradiya). We agreed and after a week of installation, the issue was back.
That was when we decided to get new brake pads and disks from Honda. Got them installed and it's been a year now. Still work like they should. Enjoying the new brakes. My rear brakes are still fine and working okay. Just the front ones wore out.
The new ones from Honda costed 16000 PKR last year. Now it's up to you if you want to spend a little more money on quality brake parts and be tension free or keep trying the JUGADS our local mechanics will tell you about and have a constant headache.
Hope this helps 