Well, junior, I�m not sure if you are winding AB-ers up or not, so here�s a serious reply which I hope will help.
The law says that to ply for hire a driver and vehicle must have a �Hackney� carriage licence. Additionally almost all local authorities now licence �private hire� (i.e. mini-cab) operators and their vehicles. Although licensed these drivers may not ply for hire but can only take pre-booked fares. These laws are administered mainly by local authorities, but national legislation sets out what taxis and private hire vehicles are allowed to do � it is not subject to local variation.
As far as I can see (though I may be wrong) Hackney Carriage offences do not carry an endorsement. However, as has been pointed out, plying for hire almost certainly invalidates your motor insurance and, although you have not said so, I suspect that driving without insurance is the basis of your conviction.
Driving with no insurance carries a mandatory endorsement and either a disqualification or between 6 and 8 penalty points. So to answer your specific questions: Yes you can appeal against the conviction or sentence.
This must be done within 21 days of conviction.
Yes, you can be disqualified (but you have not).
One aspect you may not have considered (or not mentioned) is that, by accumulating 6 points within two years of passing your test your full licence will be revoked. This is done by the DVLA, not the court, and they may not yet have contacted you. You will revert to provisional status which means another driving test (both parts). You cannot appeal against this � you can only appeal against the offences which attracted the points.
I cannot see that you have been unfairly treated. The sentence seems in line with sentencing guidelines. However, if you�d like to tell me why you think you�ve been unfairly treated (that is, differently to anybody else in similar