Answer by Paul King, computational neuroscientist:
Meditation is definitely not "bullshit."
The skepticisms raised in the question details are reasonable questions to ask, and in many cases there are answers.
In terms of a neuroscience view, if one has the patience for it, one can wade through the 870-page book Zen and the Brain by a neurologist, which is packed with technical detail about the brain and meditation. While it is dense with detail, it may lack a coherent thesis, but that is mainly because meditation isn't fully understood yet. Still, there is a lot of information in there.
As others have said, one can reasonably be skeptical of claims that meditation will solve your problems.
But what is meditation, anyway?
Meditation, for example, staring at a wall and focusing on your breath, is really "calisthenics" for attention management. You cannot "make" yourself think or feel different things. But what you can do is develop the mental capacities for managing your conscious state, which includes attention and the contents of consciousness.
Meditation training revolves around a fundamental paradox that shapes our experienced reality: to be in control you need to let go of control; and the way to be free from the mind's reactions is to develop automatic skills for noticing them, which become an alternative to reacting.
What are the benefits of all this?
Peace of mind and self-actualisation. But learning meditation can be pretty unpleasant. I have only tried it briefly myself. So far, I have not attained the necessary patience!
How does it work neurologically?
This is still being studied. My sense is that what is happening is one is training the feedback circuits within the brain to generate distraction-resistant self-directed conscious states that can flexibly reframe perceived reality. From there, the feedback circuits can be further trained to further develop this ability. The process at its best gives the owner of a brain some opportunity to influence and shape its conscious states in ways that can be powerful and empowering.
Will it help you make more money in the stock market? Probably not. Will it develop you into a more inspiring leader and someone your friends say has become nicer to be around? Probably.