As long as you still know your username/email address and password (or have Minecraft set up to log in automatically) there's no problem, all the updates are free.
If you've upgraded(?) your Minecraft account (username to login) to a Mojang account (email address to login) then you're probably ok even if you've forgotten your password as long as you still have the email account.
Otherwise you might need your receipt or something from when you bought Minecraft in order to get up and running again.
To my knowledge you can download Minecraft from minecraft.net but I think you have to log on with your Mojang account. When you start the game you have to log on with your account as well. As long as you know what email you used when you registered the Mojang account you can change the password.
On minecraft.net there is an option to migrate an old “Premium Minecraft Account” into a Mojang account. I don’t know anything about that old type of account.
EDIT: I hadn’t seen the previous post when I composed and submitted mine. Just ignore my response please!
I don't think you need to login to minecraft.net to download Minecraft, they still have a free demo mode, which I'm pretty sure is the same program, it just keeps you in demo mode until you login in the launcher.
By the way, the Windows-10 edition isn't the PC/Mac (Java) version of the game, it's Bedrock (mobile/console version) for Windows-10 PC's.
You can probably still get the Win-10 edition for free, having bought Java Minecraft before last October, should you want to try it out or play together with somebody who plays Bedrock.