Courts are open to the public and the press. Their proceedings may be freely reported except where the court makes an order preventing publication of some, or all, of the details. This would only happen where the defendant was a minor or, for example, where publication of the details could prejudice the proceedings of another court case. Otherwise there's no way that publication can be blocked.
Employers are only obliged to report criminal proceedings to their employers when they're under a specific duty which is defined in their contract, or when they're subject to a professional code which imposes similar conditions.
Employees can't (or, rather, shouldn't) be dismissed for something which happens outside of work, except when it results in a 'loss of trust'. Please see my post (together its associated link), here:
http://www.theanswerbank.co.uk/Law/Question572 429.html
A Section 39 offence is normally 'summary only', which means that it can only be dealt with a magistrates' court, not in the Crown court. (The only exception is when the offence is racially or religiously aggravated). The maximum penalty is 6 months imprisonment and/or a �5000 fine. In practice, most offenders receive a non-custodial sentence, e.g. 100 to 200 hours unpaid work.
Chris