Hi,
Let's get the sub domain/sub directory question out of the way first. Rand did a Whiteboard Friday on this recently which answers everything you could ever wish to know so take a look. (The answer is sub directory by the way.)
Now, let's look at the trickier part of your question. I understand your concerns but I think you're looking at this the wrong way. Using headline, aggregate data from your analytics really won't give you any insights which you can use to improve the performance of your website and business. All this data will tell you is how all of your visitors (those from organic search, paid search, social, email, display etc) are behaving on your site. This type of person doesn't actually exist in the real world so there's nothing you can do to improve their experience on your site.
A much better way to look at this is through data segmentation. People who are aware of your brand, have visited your site multiple times before and are arriving on a branded organic search will behave completely differently to someone who has just seen your brand for the first time on Facebook. This is totally normal behaviour. By far the best person to learn from when it comes to data segmentation is Avinash Kaushik who has a blog called Occam's Razor. There's a ton of great stuff on his site which I won't attempt to replicate here but suffice to say that by breaking your traffic down into segments, you'll be able to really easily and quickly see how improvements can be made to your site to suit each individual channel.
If you're reporting into someone, it's really important you set realistic expectations from the outset (I know this from personal experience!). Create a report which breaks down your traffic by segment so you can quickly and easily show how each channel behaves and so you can show what work you can do to improve metrics for each. Honestly, they'll love you for this!
Try and think about digital marketing and SEO in the same way you would as traditional marketing. If more people come to your off-line shop but don't necessarily buy something on their first visit, is that a bad thing? Definitely not! It's the same for people visiting your website from Facebook. You're building brand awareness, putting your content/services/products in front of more eyeballs which can only be a good thing. Google will never penalise you for that kind of marketing activity. Making more people aware of your brand is also a great way to attract organic links - another thing Google wants you to do.
I hope that helps but let us know how you get on.