She calms down only after someone of us comes to her and pets her.
If you respond to her meowing by giving her attention, then you are teaching her to meow for attention. This is a negative feedback loop of your own creation. You're rewarding her when she meows for attention while you're hoping that she eventually stops meowing for attention.
Without a clear incentive to stop doing so, the cat will never learn to not meow.
As a simple example, we had a cat who would meow by the sliding door. Telling the cat off didn't work and we tried this for months. So I devised a lesson that the cat could learn. I would squirt some water in his direction whenever he meowed, but I would do so sitting on the couch, where I did not have direct line of sight to the cat (the back of the couch block my vision).
The only way I would know where to aim (it was a wide sliding door) would be if the cat revealed its position by meowing. Without any meowing, I would be unable to aim it at him.
The first few days, he made it a game of sitting in a new spot and trying to meow then, but he quickly learned that I could home in on his position by his meows, and once he realized that, he stopped meowing.
You need to do the same for your cat. Create a situation where meowing is either a drawback, or wasted effort. In your case, it seems better to go for the latter, and simply ignore the cat.
If you're worried that something might actually need your attention when it first meows out of nowhere, feel free to go and have a look but do not interact with it. Don't greet it, don't talk to it, nothing. When you see that there's nothing wrong, walk away and don't come back.
At best, you can call the cat from where you are, to make her come to you. She will eventually learn that there's no need to meow first if she can just walk up to you anyway.
Her favorite sleeping place is by burying deep inside my mother's lap. If my mother is not there, she sleeps either on my arms or my grand mother's arms.
Cats like warm spots, that is well known. Body creases (armpits, elbows, hips, knees) are literal hotspots on your body.
Additionally, cats can have favorites. All our cats have a clear favorite between me and my girlfriend - and it's not always the same person. For example, as I tend to watch TV (without moving) more than my girlfriend, the cats favor lying with me during the day (even when my girlfriend is sitting next to me). However, at night I have a habit of tossing and turning whereas my girlfriend doesn't, and thus the cats favor sleeping on her side of the bed.
These aren't absolute statements, but we can clearly see a general tendency to be around me on the couch and around my girlfriend in bed.
I see nothing weird about your cat's behavior. She seeks warm spots, likes affection, and has an ordered list of preferred sleeping spots.