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We should have to go for keywords that people look up for. This is my secret of gaining more traffic

Correct you should make sure is not used elsewhere. But I can't refrain from stressing again to hide the content is unlikely the best strategy.

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I would buy it and keep it as a separate site. If he's buying links it might get penalized eventually so i would look to see how shady the links are and anchor text percentages before buying and ask to see their GA account so you can see if their traffic has remained strong. 301'ing a site that has been doing grey hat link building to your white hat site, i probably wouldn't do that.

Ok, this is tricky one Brad! There are situations that you should consider before you go ahead and start doing this, but before everything just go to your Google Analytics and see how much search traffic you are receiving to your design studio page and what keywords are they using to search your page. If good %age of people who are landing from search are using your brand name then I think you can go with it but if they are using specific design studio related keywords, this action can really hurt their user experience. In my opinion you can also test this idea by adding 302 redirect for few days instead of 301. If things works well for you then you can always change from 301 to 302 but if you see bounce rate is increasing or something you can always change by removing 302 and then the new page you have created, 301 it to the design studio page. It’s difficult to say how people will react to it but testing the stuff (while being on the safe side) is a good idea.

It looks like this site has a lot of backlinks for "custom t shirts" and I see them at #8 on Google.com for this term.  You'd think they would have been affected by Penguin. Here's my theory.  According to ahrefs they really started a linkbuilding campaign in September of this year. Now, Penguin refreshed on October 5th.  It's possible that at that time they didn't have enough exact match anchor links to trigger the filter.  (We're assuming that this is the major component to Penguin). My guess is that they'll decline with the next Penguin refresh. Now, Penguin doesn't necessarily pick up paid links, just unnatural linking patterns like gross overuse of anchor text. In many cases, to be busted for paid links a manual spam review would have to be filed.  Personally I would not file a spam report though.  I think what goes around comes around.  I'd spend the time working on my own site and see what happens with the next Penguin refresh.