#1

As we dump in a lot of existing Markdown content, most of it has an initial # or ## heading. It would be good to show/hide this via a global or then vault specific preference setting as the file name is already most likely reflecting the contents.

#2

Is custom styles in obsidian.css an option for you?

#3

That would also work, best if across all custom and default styles. Seems I switch CSS once a week for the same vault.

#4 
/* This should hide first H1 tag in notes */
.CodeMirror-code > div:first-child > .HyperMD-header-1 {
  display: none;
} 

/* This do the same for markdown-preview */
.markdown-preview-view > div:first-child h1:first-child {
  display: none;
}

EDIT: Update the code for preview mode.