In CA, a lawyer's motion to withdraw is routinely granted, and all the lawyer has to allege is your non-cooperation or a breakdown in communication --lawyers aren't compelled to represent someone they can't work with. If you oppose the motion, that will show that you had notice of it, and if you appear at this hearing, the lawyer will argue that you had notice of the motion being granted, and the order will take effect that much more quickly. if you don't show up, the order granting the withdrawal will take effect after you're served with the order, probably 30 days later.
As for your strategy of filing a demurrer, demurrers cost money to prepare and have a hearing on, and often they do no more than educate the plaintiff about something they can easily fix. Many lawyers think they're a bad strategy unless the complaint isn't fixable and can get dismissed on the 3rd or 4th demurrer.
If your lawyer claims you owe him money, he has to give you 30 days notice of your right to arbitrate any fee disputes before suing you, and for $1,000, he might not bother. You have 1 year from the date of injury to sue him for legal malpractice, but on these facts, it doesn't sound like you have a case, since this demurrer/answer dispute isn't grounds. Under CA ethical rules, your lawyer has to promptly turn over your entire file to you or your new lawyer, whether you owe money, or he claims you do, or not. You may also want to review your written fee agreement for your rights vis-a-vis your lawyer.
You're probably best off with a new lawyer that you can trust, so you should be looking for one now.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
The law of your State and rules of civil procedure will govern how to proceed. Generally, a motion to withdraw is a short hearing in which the lawyer and client show up in court. The reasons for the withdrawal are set forth in the Motion to Withdraw.
Because it sounds like irreconcilable differences exist, the court will often not delve much further. Remember, all communications between you and your lawyer are confidential and privileged, so the court really cannot get into much detail. It is important that you try to keep confidential any legal advice communications you had with counsel, without discussing them in open court. Otherwise, you may be waiving the attorney client privilege, which is generally not a good thing.
The court often grants these motions, and gives the party -- you -- time to find another lawyer. You should ask the court for the amount of time you will need, say 60-90 days. Generally, a court will stay the proceedings (i.e. put them on hold) while you find another lawyer and that attorney gets up to speed. This prevents the other side from taking advantage of the brief interruption in representation.
As far as the merits of your dissatisfaction, it's really hard to get into who is right and who is wrong without complete info (i.e. every dispute has 2 sides). I would say that as far as an error regarding the entity type -- LLC vs. DBA -- in my experience this would not result in dismissal of the complaint. Most court rules permit a plaintiff to amend the complaint at least once as of right to correct things like this.