There is no direct linkage between failing to appear and having your request for a prayer for judgment continued granted. Regardless of the history of the case, it is always up to the judge whether or not to grant that request, and every judge has different personal policies for what requests they will grant and under what circumstances. Certainly there is a possibility that the court will not grant your request because you failed to appear, but in my experience that is rare. You also need to be aware that your summary of the various costs and fines for the case is probably no longer accurate. If you get a PJC then you would not pay a fine, just the court cost. But the court cost has likely increased due to your failure to appear. There is the possibility of a late penalty being assessed ($200) plus fees for issuance of an order for arrest or jail fees, each of which would be added to the cost.
No answer to these questions is intended to, nor does it, create an attorney-client relationship. There is no substitute for an actual conversation with a licensed attorney about the particular facts and circumstances of your case.
You do not need an attorney to ask for a prayer for judgment continued. A request for prayer for judgment continued would be made after you enter a plea of responsible to a traffic infraction or guilty to a misdemeanor traffic offense. It is in the judge's discretion whether to grant the prayer for judgment continued. Keep in mind that with a prayer for judgment continued you will not face a fine for the traffic offense, but you will still be obligated to pay the court costs. It sounds like money is an issue here, and you can request the judge remit the court costs based on your financial situation. Both a prayer for judgment continued and remission of the court costs will be in the judge's discretion after you have admitted guilt.
The Failure to Appear will add to your costs and fine. You can ask the judge to strike the Failure to Appear for good reason, saving you the additional expense. You do not need an attorney to request the Failure to Appear be stricken.
These comments, based on limited information, are not intended as legal advice and are not to be construed as creating an attorney-client relationship. For legal advice consult with an attorney to get a thorough review of the charges.
You can ASK for anything. However, when it comes to traffic tickets, citizens normally come out much better in the end if they hire a good attorney (less court costs; less DMV points; less insurance costs; etc.). If you hire a good attorney, at least you know you will get the best possible result.