Below are some detailed edits ... the first part of the story (to the first ***** break). I ran out of time to do the rest, I'll try to get to them tomorrow.
Spoiler:
"but even souls" -> "but even our souls"
The first sentence of the first paragraph seems at odds (contradictory) with what follows in that paragraph. (You say you were "submerged in utter grief", and then proceed to tell us that you're only offering a "pretension of grief".)
"... all these happen?" -> "... all this happen?"
"Later on I wondered ... only for twenty-four hours." -> consider simplifying this paragraph so it reads more smoothly and to avoid tense problems. For example: "I wondered if I was being unnecessarily curt with him, but then I was not feeling that great myself and was in no mood for conversation, especially with someone I had known only for twenty-four hours." (If you want to leave the "later on" prefix then the present tense - "was being" etc. - is inappropriate.)
"... than she'd normally." -> "... than she would normally." Just a suggestion, the abbreviation feels wrong to me in this context.
"All of a sudden, the sound of clattering stopped again." -> "All of a sudden" doesn't read well here, I think something like "Abruptly" would work better.
"... - all within a couple of seconds" -> seems redundant to me.
"I then told my mother than I can't sleep any more in darkness; she agreed." -> There are a number of issues here. You could trying using actual dialogue, or try something like: "I told my mother that I couldn't sleep any more in darkness. She agreed."
"...; moreover, I didn't want to disturb her sleep." -> seems unnecessary.
The three paragraphs starting at ""Sunshine would, in just ..." seem overly verbose and awkward. Try to tighten them up a bit.
"As we two were talking among each other in the ..." -> "As we two were talking in the ..."
"I chill ran down ..." -> "A chill ran down ..."
"She later proposed that there was no need to keep the kitchen light burning too even when we were done with our cooking." Does this matter to the story in any way? If not, delete it.
"He went off to his room, and from what I could figure, slumped on his bed." -> "figure" seems the wrong word in this context. Did you mean "hear", perhaps?
Review all your uses of "etc." and make sure you really mean to have them (for example, it may be a mannerism of _one_ of the the speakers). Where not essential, try to get rid of them. I also suggest spelling out in full rather than using the abbreviation is better.
The four paragraphs starting at ""Oh, I see. If you don't mind, I'd like to know more ..." feel a bit stiff and awkward. In particular, try to cut down the very long paragraphs. For example this "wander aimlessly from place to place, finding no abode or solace, suffering all the time, unable to take birth as another being on earth, etc." could possibly be reduced to something like "wander aimlessly from place to place, suffering all the time, and unable to be reincarnated." (And the "- in other words..." trailer is not needed at all, I think.)
By the time we reach "As we didn't know how to perform the necessary rites ourselves..." we've been away from the conversation about shradh for a while, so something like "...necessary rites for shradh..." would help.
"burning - both literally and figuratively - throughout the night." -> Why "both literally and figuratively" ?
"... she mumbled to me that the shradh needed to be done ..." -> ... Mom mumbled to me ..." (We need an attribution here, I think.)
Does any of the paragraph starting at "In the meantime we continued to live as usual ..." actually matter to the story? If not, I suggest the first part of the story could finish well at the preceding paragraph.
I have some quibbles about the punctuation, but mostly I haven't made explicit comment about them, there are enough other comments to be going on with.
Things are definitely clearer to me this time around (although some of that will come from knowing what to expect). The additional explanation for shradh is a good thing, but as noted above it needs to be tighter, in fact this entire first part would benefit from trying to cut it back to essentials. It is, in essence, only scene setting for the important part of the story still to come, and so you need to keep it as brief as you can manage.