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My vote goes to Yoast. I do urge you to manually review the SEO of your site as well since any plugin cannot optimize your site entirely.

While I agree with your advice, I am not sure that getting rid of more links right away is the right thing to do.

@David

Without knowing the entire story of this site, it seems to me that your appearance on page three indicates that the penalties are no longer affecting your site as it has positively improved. I think in this case spending your time trying to get some very authoritative and trusted links would do you the most good. Remember, most sites have spam links pointing to them for one reason or the other but if those links make up only a small portion of the total link profile, they often do not harm the site. If this wasn't the case negative SEO would be the only way people boosted their own sites.

Good luck and keep at it!

I wouldn't worry to heavily about getting FB likes for that type of business. Do you have a strong presence in the local results for your area? I would focus my efforts on getting those many satisfied clients to leave a review for you on Google, Yelp, etc.

If you really want to grow on FB you could try a contest or special offer for future clients, both of those methods work pretty well.

Keep in mind though, you are getting FB likes to advertise and interact with potential customers. If the likes are just for the sake of numbers, it isn't worth it.

Just for the record, you can rank your website without any social signals.

It would be best to lightly revamp the poor content on site that is ranking for the important key terms you are targeting. In doing so why not just write a lead in or make reference to something on your main website to encourage click through traffic. By doing this, you will likely help to maintain the good rankings for the new 'junk' site while generating referral traffic to your main site. Additionally, a site ranking well for your target terms linking to your main site could be beneficial to your rankings.

You could re-write it to be http://www.nlpca.com/DCweb/modelingwithnlp  but you don't have too. What are you trying to accomplish with this page?

I have to agree with you Andy. Avoiding the hassle of having duplicate content issues makes it worth no-indexing.

Which platform you use really depends on your business. Will you have a lot of images to share, etc. I would suggest that you try to build a following on Facebook, Twitter, and G+, but definitely on Facebook. The Moz guide to social media is a good place to start.

http://moz.com/beginners-guide-to-social-media

You do not have anything to worry about it these links are all no-followed. They are even helpful for the sake of diversifying your no-follow vs do-follow ratios. No follow links have been proven to pass certain metrics to linked sites and this to can be helpful, so I would not change them if it was me.