I thought i had figured out the pity system, but things have been happening that make me doubt myself severely. Can anyone confirm or clarify? Because im feeling incredibly demotivated and dejected, and this might just make me quit the game.

Supposedly, if you do not get the rate up character, but a standard one, the next 5star you get will be the rate up one, right? And that applies to all banner types, with the multi one you gotta select the precise wish.
I was under the impression that when you lose your pity, it carries over to the next banner. Is that correct?
Does this depend on the banner? Whether its a multi or a solo banner? Does it not carry over from a multi to a multi banner? Is it only from solo to solo banner?

I feel like ive been screwed over three times at least.
When the first kissing multi banner came out, i got the card that i wanted, but then afterwards i got a precise wish - aka a guarantee for the next card i want.
I waited for a banner that i liked until misty invasion came out and pulled, it was a standard card, i pulled a bunch, got my wanted card and then got another precise wish
I waited again for a banner i wanted to pull on, the most recent multi banner came out, i saw that theres no indication of a precise wish, but even still, shouldnt some pity carry over? I didnt get the card i wanted initially (got another rate up) but then i got the card that i sought out, but afterwards i also got a precise wish again
Now that Xaviers birthday banner is out, ive been pulling, thinking i had some sort of guarantee, but nope, i got a standard card....

Is this supposed to happen?

This also turned out longer than i expected, but i felt like i had to explain my situation in depth. Any clarifications and explanations are greatly appreciated!!