"Will clients still want to work with you even if you increase your
rates, based from your experience?"
Some will, some will not. But if you never change your price, how will you know? As a rule of thumb, when you are 80% fully booked, put your prices up. When you are less than 20% booked, put your prices down. You keep doing this, and you keep testing the market. You might be surprised at what people will pay. People that want to pay the least are not your ideal customers.
The real world is a bit more sophisticated of course. I have two customers that keep me afloat, that use me constantly, and I have a great relationship with them. They get a bargain from me, and account for at least 50% of my time. New customers, if I am excited by the role, get a great price, if I am not, they get a higher quote. If I really do not want the work, they get a ridiculously high quote. Sometimes they get accepted and everyone is happy, I get a great fee, they get the developer they wanted. Even if the role is a bit boring.
I would never start a project without prices, timescales and objectives being laid out in advance. If they are late paying, I charge them. If they are late getting requirements to me, the project goes on hold, if they want to change timescales, I charge them, if they want to add objectives, I charge them. If they want to drop things, great, but no change in price. You would be surprised how this approach is actually respected and seen as professional.
You must vary your prices. You must try and move up the ladder of price points, otherwise you will always be scrabbling around at the bottom of the pile working for pennies.