The duration of the transfer depends of the extension of the domain. As a reference, a domain .COM, .NET or .ORG will last 5 to 7 days. In the case of an .ES the duration can last 15 to 30 minutes once it has been accepted for the administrative contact.
During the transfer process the domain will remain operational at all the time.
If keep the DNS the process will be totally transparent. In the case that you assign others DNS or you contract a hosting once it ends it will point to the DNS the hosting will be activated and you will have create email accounts and / or upload your Web to the server.