the world will be yours, sweetling

Why did littlefinger love cateyln and not lysa, do you think?

Well, I don't think Littlefinger ever genuinely loved Catelyn, for starters. Even as a teenager I think that was puppy love that turned very sour when the reality of Catelyn being a real person who exists within the constraints of a society began to bite.

But as for why Littlefinger always wanted Catelyn more...

Again and again and again, that's people acknowledging that Catelyn's clever and interesting and tough and also good-looking. Attraction varies, but it's not that hard to see why Littlefinger would find clever, argumentative Catelyn more interesting than Lysa.

Hi! I really don’t understand Sansa’s reaction to ser Hugh’s death in AGOT - the “strange fascination” thing. Especially when she reacts so strongly to other people’s deaths later. Is she in denial because of the general splendor of the tourney, stuck in Stoic Lady Mode or just unempathetic/cold? I don’t get it, may I ask how you make sense of it?

At that point in AGoT, Sansa's already doing some mental contortions to deal with Joffrey and her impending marriage to someone she knows deep down to be...Joffrey. Specifically, she's thinking of life as a song. Her second chapter is actually fascinating to me for the dreamlike quality of her narration, and those moments where Sansa rather abruptly snaps out of it , where events diverge too greatly from her internal narrative (her first meeting with Littlefinger, Robert's argument with Cersei, and most notably her experience with Sandor Clegane). Ser Hugh's death is a moment in that song, one of the unpleasant and scary bits, but able to be understood and dealt with because it isn't quite real.

Later, Sansa is all too aware that this is real.

If Lysa is so unpopular in the Vale, how does she keep power for 2 years? Especially with Yohn Royce (and others?) eager to join Robb’s cause? Wouldn’t there be Lords Declarant (same guys as in canon or otherwise) eager to “ease” the grieving widow’s burden by removing her as regent? Because it kinda feels like GRRM pushing his thumb on the scales so there’s a pro-Stark army on reserve for later books.

Let's have a look:

Brynden's misread that slightly - what's going on is that Lysa's playing off all her suitors against each other. While several individuals believe they have a chance with Lysa themselves (and therefore of accessing her use-rights to the Eyrie, her relationship to her son the heir to the Vale, etc), they're not coordinating to remove her from power. As we see in ASoS and AFFC, the coordination only really begins once Lysa's remarried.

In addition to this, what we see of the Lords Declarant in canon shows them to be a stuffy, snobby bunch, who don't seem to question at all that there should be an Arryn set up to inherit the top job. The 'proper' arrangements mean a lot to them, and interfering in that by forcibly removing Jon Arryn's widow from her position as guardian of Jon Arryn's son is a Big Deal.

It's absolutely GRRM putting his thumb on the scales to keep the Vale's resources in play for later, but there are Watsonian reasons everything played out as it did.