Scrolls is free on Android devices. Does it mean I have to buy it again?

On the Google Play store listing, Scrolls is listed as free; meaning that it can be downloaded to any device and played straight away (after installation of course).

But, Scrolls is not free. (Note: You'll need a Mojang account for this link to work, otherwise it'll ask you to login. It is a link that lets you buy Scrolls)

According to the store page listing, it says the following:

FREE VERSION - The full game is available from the ingame store.

And I can't seem to find a paid version anywhere else on the store.

I for one, already own Scrolls on the PC. Will I be able to simply login with my Mojang account and play the full version straight away... Or:
Do I have to purchase another copy, which will be binded to my tablet (or Google account)? Or will I have to create another Mojang account?

I'm asking because I don't have the net connection to download it at the moment. And the last time I tried resulted in an incomplete package; app wouldn't properly install.

No, you do not need to rebuy the game; the full game can be unlocked by logging in with a Mojang account that has the game activated on it.

According to scrolls.com (Mojang's official site for Scrolls), the game only needs to be purchased once, as it links to your Mojang account.

Scrolls is now available for PC, Mac, and Android tablets.

If you’re new here, welcome. Click below to try Scrolls for free. If you like it, you can upgrade to the full version in-game for $5 USD/€4.50 EUR/£ 3 GBP.

If you’ve already bought Scrolls or participated in our Alpha or Beta test, the full version will be automatically unlocked. Download below, then log in with your Mojang account.

The quote is from the site linked. It is a post about the release of scrolls for tablets.