Well something is running search queries from your machine or network. Moz does not operate from your computer/network but from their own servers in the US and it will never affect your machine, its physically impossible. You need to find the issue on your machine, and I would start with investigating the browser environment first - plugins, addons, running fresh instances of the browser as Ryan explained above and if it doesn't help moving on to other software you have installed on this machine. You will find it eventually... Good luck

This is pretty disturbing news actually and it doesn't make any sense to me. If Google wants to promote pages with more and better quality content above the fold but also clean pages that users like - the read more buttons were the only functionality to marry both concepts.

At the moment all my pages are still fully indexed but if I see this change come into life I will have to re-think the content and layout of many pages...

There is no golden rule but generally yes, the page higher in a structure would be considered slightly more important, especially if your sitemap indicates page importance automatically, but a proper structure has far more benefits.

As long as you don' overcomplicate your structure it wouldn't make much difference whether your roses are at:

domain.com/roses

or

domain.com/anniversary-flowers/roses

as for no 4 - could it be that roses would fit many of the categories and therefore have been taken out of the structure to avoid duplicate content issues?

I often see pages deeper in the category tree ranking just as high if not higher than top categories for their respective keywords. At the end of the day Pete, it's the content that will rank your page not the url.

Using common sense, do you think Google would promote a model of websites where all pages and categories are always in the root? Would you use a library where all books are stuffed into 1 section? I don't think so.

This is very often overlooked but in my opinion the right URL structure is critical for any site, because the on site optimisation and content creation for landing pages will be very much determined by the structure of your URL's. Logical structure also helps users understanding and navigating the site.

I always suggest a "library" approach, so creating a logical structure similar to a library where a book (or a product/service/article etc.) falls under one parent category, which falls under a higher parent category, similar to:

science-books/physics/newton-inventions

entertainment-books/childrens-books/harry-potter

I your case the first example of URL path makes more sense, but the question is - are dozen roses only anniversary flowers? Spend a few hours organising your products into categories that make logical sense and create a URL structure to reflect that but keeping in mind the keywords people are searching for to find your products. It's not easy so don't rush it.

Ah and use hyphes (-) rather than underscores (_) in your urls...