If you negotiate your salary in the first interviews you can certainly lose a job offer. Asking the salary range for the position is as far as you can go. It would be fine if the job posting didn't already specify the number. As mentioned above, I wouldn't even bring up the salary issue until you're in the final negotiation. And I don't think there's any harm in telling the interviewer that you want to be paid fairly. They may not know what other people are making, so they may not know if you're being underpaid.
I have no idea what the market is like in your area, but if you're being paid less than the market rate, you should probably quit. I'm not saying you should quit every time you're underpaid. But you certainly should quit if you can get paid more elsewhere. If you