Ps4 – If I purchase a PS4 console with online games already bought and want to use the own PSN account, will I lose the games

You will need valid billing information for the region matching your PSN country. Since a Qatar account is out of the question apparently, I would recommend the US store if you are fluent in English; the US store has more variety than some regions, isn't in Japanese, and I believe the UK/EU stores are a bit more expensive in some cases.

You should be able to use a prepaid credit card (which won't require actually opening an account in that region), this forum thread indicates mixed but mostly positive success, I believe they only recognize Visa and Mastercard numbers on the store. Any prepaid card with a proper credit card number (16 digits, recognized as valid) should work, though I haven't tried this myself.

Note that to actually purchase items on the PSN you will quickly run out of money on that prepaid card, but you can use special prepaid PSN cards (I am unsure if these are region locked, but US ones should be in good supply to import?) to add to your account without a real credit card.

First to check to see if you're actually using the same account on both consoles. The fact that you can't see your transaction history makes me suspect that you might have created a new account for your PlayStation 4 instead of reusing you existing account.

Otherwise in order for a game that you bought from the PlayStation Store for the PlayStation 3 to be playable on your PlayStation 4 two things need to be true. The first that there must be a PS4 version of the game. The PS4 isn't backwards compatible with the the PS3, so any game would need ported to the PS4 for you to play it on you new console. The second thing is that the particular "product" you bought needs to include both the PS3 and PS4 versions of the game. Most games aren't sold with both versions bundled together like this, so you need to buy separate versions for each console. Most developers will want to be paid for the work they had to do to port the game to the PS4, so this shouldn't be too surprising.

For example, Assassin's Creed IV Black Flag is available on the PlayStation Store in both a PlayStation 3 version and a PlayStation 4 version. These are separate products you need to buy separately. An example of one of the few games that you can pay one price and get the PS3 and PS4 versions, along with the PS Vita version too, is OlliOlli.

If you look at where it says "Playable On:" on the store page you can see the difference between the games:

There also the PlayStation Now service you may have heard of. This service lets you play games on your PS4 (and other Sony devices) by streaming them to you console. This works by running the games on Sony's servers (modified PS3s) and streaming the video output to your console. Unfortunately your purchase of games on the PlayStation Store doesn't entitle you to play these games on PlayStation Now. You have to pay a rental fee if you want to play them using this service on your PS4 or other device.