to answer the 1st question. Of course a CMS can affect how website performs. Meaning some are built better than others. If you had a CMS that was to produce all flash content that would be a pretty bad CMS.
I honestly prefer WordPress it works beautifully with search engines as well as people. The important thing though is that you can create a website that is easy for the end user and accomplishes what they want because that's exactly what Google wants.
when I used a tool I use a lot from Internet marketing ninjas in order to scan your site for issues it was giving me a 408 error that error is
- "408 Request Timeout (Couldn't find the user in time)"
- you can see what I mean right here I attempted this 8 times.
http://www.internetmarketingninjas.com/seo-tools/google-sitemap-generator/tmp/772958e055a835d23c6db867963439d1.html
I used a another tool screaming frog SEO spider I highly recommend this tool it is free for up to 500 pages though the Pro version gives you the ability to fix a lot of problems instantly.
http://www.screamingfrog.co.uk/seo-spider/
Here the results
https://app.box.com/files/0/f/550482746/1/f_11967719472 crawl overview
https://app.box.com/s/nvyyszluy9mb9rhx1ms6 redirect chain check
https://app.box.com/files/0/f/550482746/1/f_11967725394 all links
I would doubt the CMS has anything to do with your issues. Based on using this tool below called feed the bot
http://www.feedthebot.com/tools/spider/test.php
I was able to crawl your site with no problems. That replicates googles ability to crawl a website. If there was an issue with your CMS blocking Google bot I would've picked it up there
It seems your CMS is custom-made I have never heard of this particular one however that does not mean it's bad. I would recommend using WordPress if you you build the site for any reason. It is very search engine friendly and has a extremely large pool of developers.
Use some of the tools found in this link to scan for other issues
http://www.feedthebot.com
aside from that I would guess that your prior penalty may have something to do with a drop or he could be the lack of content one your site. Overall you do not have a lot of content meeting over 200 or 300 words per page I would start by issuing another question regarding whatever you find to be off about your site. Or something more detailed about what exactly you suspect is a problem why you think it's your CMS? I would really love to hear some more info about this I hope the data I've provided is able to tell you that I do not believe it is your CMS that is harming you.
Download screaming frog and use it
sincerely,
Thomas