My initial thought is that companies that offer services that single people might want to use won`t specifically say "Hey, single people over here! You need us!" This goes against the American cultural desire to be independent. But plenty of companies will talk about how their services or products will save you time and hassle, which is something a single person would want. It`s just indirect. To address your specific examples:
Car`s in the shop--some shops DO offer a loaner, especially the dealerships. Enterprise will pick you up from a shop and take you to rent a car. Or there are taxis.
Pet care--plenty of people are available to stop by your house and feed/walk/play with your pets while you`re away. And this isn`t just a concern for single people--married couples often go on vacation together! :D
Plumber--yeah, I think you pretty much have to wait for them. And this would be the case if you were married, too. Someone has to be there. You could ask your boss to let you telework on this day.
Travel groups--I don`t know for sure, but I bet you could find something like this online. It might be marketed toward senior citizens, though. I think this is the example of the five that seems most ripe for new ventures.
Hiring a manager--as Craig said, there are concierges. There are also maids and secretaries. And if you really want someone to be in charge of your life, make a lot of money and hire a personal assistant! :D
What you may be sensing a need for in the marketplace is a resource where all of these services were made available in one place, like a website. I could definitely see a website about making life easier for "singularities" being popular. I don`t know if any already exist.
Also, I addressed my comments to "you," but I`m not assuming that you, Karel, have all these problems. I`m just speaking generally.