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Yes, Hover was created in 2008 and is a subsidiary of Tucows, which is a well-known and credible domain registrar service.

It depends on the type of TLD you're looking for, a .com domain for example costs $12.99/year to register.

Hover doesn't take fees for transferring the domain per se. However, they do take fees for a 1-year registration which is officially required by the ICAAN upon any domain transfer.

You can contact Hover’s customer support via live chat, phone call, or by an email and ticketing system.

If a domain wasn't renewed within the grace period and wasn't purchased by someone else, a restore feature is available for users to attempt to get hold of their domain which is available for 30 days after the grace period had expired. This window of time is called the redemption period.