Hey, like college, everybody experiments once in a while. I won't hold it against them lol

Because I can't think of any Sony handheld game that would do particularly well on the 3DS. It's just not worth it in my opinion.

Are they selling particularly well on Vita?

Because I'd want to combine the strengths of both companies, not their weaknesses.

I don't see Sony as a company going third party because they have the ps4 and its doing pretty good but the vita not so good. They should go away from portal and stay with consoles.

You lost me in the second sentence. What is this "Sony games" you speak of and what does it do?

No, but with the Vita it's their system they have to at least try and help it. They aren't making games on Vita for profit. They are making them to make the system more desirable. That's why I think making games for the 3DS would just be wasting resources for little profit.

Or Sony stops with the Handheld stuff and brings those games as "PSN" Games for the PS3/4?
Maybe even connect them to an App on Android phones/tablets were you are able to access and play them.

Lets do it like that

Sony Handheld goes either to PSN or 3DS
Nintendo Console Games go 3rd Party on PS4
Xbox goes either 3rd Party for PS4 or SteamBox/PC.
All the losing ones help the others and no competition exists anymore!

Sony is not all about money in games, they make games with passion which is good and respectable. So, they try to take risks and create a gaming studios to create more innovative games all the time which can be proved from PS3, vita and PS4. Sony is not like all the time milking known IP's, they use old IP's along with they create New IP's. 

Sony always explains itsself we are the gamers who make games with passion. I'm really proud of everything they do, sometimes they do somethings which everyone hate but there will be a good reason for that and they try to explain as well to gamers. 

Also its not possible for all the Vita games(Full games and Indies) to run on 3DS. It can be possibe to make that game with so much details removed and spend so much time to code because it doesnt that horse power to make those games quickly.

This can be proved, why all the Indie developers are not making games in 3DS that Vita is getting every week? because 3DS has big user base so they can earn more money, instead they chose Vita because its easy to code and sony loves creators of games.

don't forget the DKC 1-3 ports and the Banjo games on the GBA!