As a Hungarian software developer, up to this day it is not possible to sell apps on Google Play, because Hungary is not on the merchant list, therefore only free apps are allowed to upload from Hungary.
Is it possible and legal to upload the free trial version of my app to Google Play, and when the trial expires, through an intentional and unequivocal notification / window redirect the user to my own website, where she / he, after the payment process, can get the full version?
I'm also planning to put the link of the full version app to the Google Play app description section.
You can post a free trial version of your app in Google Play and when the trial expires then they will be required to download a license file from your website.
This file will only remove the trail and let user use the app. You can add a notification when after 7 or so days of trial to purchase license. when they press okay then they would be directed to your website and download the license apk file after they pay.
And then after you post an updated version of your app in Google play. They will be able to update too and they will not loose their full version of the app.
Please make sure that you describe your app correctly in google play, and state that your app is free only for some days. and do not post a link to a full version app in your description if you are planning to host it on your website.
You can also integrate in-app purchase with the help of Paypal. This documentation teaches you how to do it.