1.) When users upgraded to WordPress 3.6 there was an error message that appears on the default comments section. Asteroid 1.1.2 fixes this. I guess those users that use other commenting systems like disqus or jetpack weren’t affected. So this is not really a crucial update if you’re not having any errors on the comment section. Anyway I’m not seeing any major modifications on your site. If you plan to make more, then using a child theme now is really the best approach.
2.) I unfortunately don’t have any device to test it on right now. You could try to visit this site that uses asteroid theme: http://gamenovice.com/
If it displays correctly on any position on your mobile device then I think it’s your own site that is causing the issue.
Your site shows a horizontal scroll bar on the bottom when viewed on a desktop screen. There shouldn’t be any horizontal scroll bars. I suspect that it is caused by the plugins you are using. You could try deactivating them temporarily and see if the site displays correctly.