How do I archive a post?
When you publish a post the software automatically Archives it - you do nothing.
And what's up with these ads popping up for instance on mobile devices?
To off-set the costs of providing free hosting to millions of bloggers, WordPress.com has been running advertising on our free hosted blogs since 2006.
10. Advertisements. Automattic reserves the right to display advertisements on your blog unless you have purchased an Ad-free Upgrade or a VIP Services account. http://en.wordpress.com/tos/
If the ads you see are found at the end of blog posts then provided you see this small About These Ads link what you are seeing is WordPress.com generated advertising.
To eliminate all advertising on our free hosted WordPress.com blogs we can purchase an annually renewable No-Ads upgrade.