In the UK, can sex-offenders attend Church services where children/under 18s go?

There is no law on this. Normally they will have a Sexual Harm Prevention Order imposed on them by the court and typically that will ban being alone with anyone under 16 (because of course 16 is the age of consent, not 18), but they're not alone with a child in a church service, are they? If someone else is there, where's the problem? If you still see that as a problem, why? Doesn't the Church believe in forgiveness and rehabilitation any more? You might as well ask if sex offenders are allowed on public transport, because children go on that. It would be impossible to frame a law on it that didn't curtail freedom so much a sex offender couldn't even go shopping on the bus.

And remember not all sex offenders offended against children. Some raped or sexually assaulted other adults. What does this have to do with them? This is why there are Sexual Harm Prevention Orders - that effectively makes a private law personal to the individual offender and what they did. Break the order and the maximum penalty is 5 years' imprisonment.

Anyway, how would anyone know if someone who just came in to a service is a sex offender? Or are you proposing that churches should quiz everyone new about this? That would be a guarantee of getting no new members.

So it's up to different Churches how they deal with it. The one I happen to know best is the Methodist Church, and it is legendary in Methodism that the answer to everything is "set up a committee". The rule is that if a local church knows it has a sex offender in the congregation, it must set up a management committee to determine what they are and are not allowed to do in the church, and have someone sit with them during services. This would probably put a sex offender off ever going there again, but that's what they do.

And of course all ministers, lay preachers and anyone who works with children are required to have an enhanced DBS disclosure. I remember when this came in and some lay preachers resigned because they felt it was an insult to be asked - of course the job only involves conducting services, which doesn't involve being alone with children. And DBS disclosures aren't the answer to everything, because they only show up if someone's been convicted or had any dealings with the police. A paedophile who has always got away with it would look as innocent as anyone.

Yes

Yes. they cannot usually be near a minor child, and that includes in church.