I run a registrar, and while we can mess with people's domains we would get in serious trouble with the registry and you would get the domain back if we did so. Many registries have rules which protect the domain owners from the whims of registrars, but if you are worried you can look it upf or your specific registry.
Whether the registrar has much power depends on the registry, usually not really (you usually can just move to a different registrar and the old registrar can not legally prevent you from doing so).
The hosting/email provider is obviously not a problem at all, as you can switch to a different provider at any time (just make sure to keep the domain registration and the service provider separate) if your current provider is an asshole--or you can just host your own server if you want to avoid any providers messing with your emails.
I strongly recommend people keep their domain registrar and hosting provider as separate entities. It makes it much less likely you'll suffer a catastrophic loss.
