@Kamal-Patel I'm on my iPad at the minute, so I can't test it, but removing unread should be possible using CSS rather than fondling core.
The width adjustments are done using js, the route to the file was posted in a thread yesterday or the day before, again, first world iPad being clunky issues, search should find it.
As for the last one, I'm not sure, the composer window seems to be called by
#new_post via an on click event, but I don't think it would work on the custom homepage. Rather than bringing categories and new posts to the homepage, could you not redirect users from the homepage into that category?
There's probably a simple reason why not that I've not seen, but Ive powered down the rig as it's 4am, so I can't test anything out.