A byelaw conviction is a criminal record, that comes with a fine, victims' surcharge and various other costs. It will be "spent" after 1 year, at least in terms of most purposes. So for most lines of employment an employer cannot ask about spent convictions and you don't need to tell them about it. Some professions in health care, government service, children, some finance and legal roles, there is a requirement to declare all convictions (and usually cautions too) beyond that 1 year. Having said that, byelaw convictions for fare evasion is towards the bottom of the list in terms of seriousness, particularly as time marches on. People get convictions for traffic offences, drink driving, even the (current) prime minister has two Fixed Penalty Notices.
Other countries, such as the USA and Australia do require convictions to be declared even by tourists. In those cases you may well find yourself not able to take advantage of online ESTAs, ETAs and the like, but will have to apply for a manual visa. They don't need need to stick to the UK's notions of spent and unspent convictions. From the various briefing papers for ETIAS, the new EU system for Third Country Nationals such as the UK, you probably won't have an issue there, but it is vital to answer all questions honestly.
For your case regarding a railcard, there is quite a consensus around your case that Chiltern are not correct in what they are doing. Whether you want to engage a solicitor to fight that case is something only you can decide, but at least in theory someone without a solicitor, but making the correct case and researching the details, should get to the same outcome, a positive outcome from your perspective.
