Robin

I know it is bad for SEO (i am using it on a pvt network 🙂 ) , but just to add it did not crash my sites, i had to use them for very specific purpose and almost 7 sub sites pull the feed from my main site

on the other hand if u dont want to use the plugin, use a script for db search and replace while dumping your sql file (it gives a GUI based interface for easy db dumping and replacing) and than do tools > export
should work fine and widgets would also be exported like this

The plugin i use to pull posts (the way you want) is through a plugin called autoblog (it is a paid one though 🙁 ) but works perfectly and has an option of nofollow too give it a try

Yes it is possible using wordpress multisite

For extracting the different posts from sub-domain on your homepage you can use a plugin called auto blog (which allows u to setup a category feed from different sub sites )

Secondly regarding using same account to access the sites, did u try installing buddypress on top of ur wordpress multisite, as it works like a social network and allows user to access your website.
and you can sync the user created on buddypress registration page to auto register for wordpress user.

you should explore these two options and it should help.

This is not a standard code for archive.php file and looks more like an eval style hack
clean the site —
would suggest re installing your wordpress again

Hi
Instead of altering the core homepage code
i would suggest you to create your own custom page and call it on home menu

you can easily create a php file name it xyz.php
and add this code on the top
<?php
/*
Template Name: XYZ
*/
?>
and than you can include the header
and write any code you want under it
and close it with including the sidebar and footer
you can replicate single or page.php