Is it permissible to open a restaurant with two sections (individuals and families) without a physical barrier between them (or with a glass partition), given that there is no guarantee that those using the family section are actually a family?

If you allocate a section for families in your restaurant, then you bear no sin for the transgressions or objectionable acts of the customers. Their sin is upon them alone, for Allah Almighty says: "And whoever earns a sin, he earns it only against himself." You are not sinful for what you did not approve of and did not assist in. And if you see an objectionable act, try to denounce it to the best of your ability and according to Islamic guidelines, for the Prophet, peace and blessings be upon him, said: "Whoever among you sees an objectionable act, let him change it."