I would not use 1x1 pixels to give links or anchor text.  That could get you in trouble with search engines for trying to hide something.

I honestly doubt that this is helping your competitor and is certainly more risky than helpful.

Just stay the course on improving your site.  You will beat them when Google thinks you deserve it... or when Google drops them for trying to hide links.

I'm a total newbie to SEOmoz and am totally addicted.

That says it all.  I am confident that you will get a lot out of it and will arrive back home with an enormous list of improvements to make.

The people who need to worry about getting their money's worth out of a conference are the people who are not addicted.  They think they can go there, sip coffee and fart, then go back home as an SEO expert.

If you look at the speakers and topics list you will see that the agenda is very impressive.  Looks like it will be time very well spent.

Shopify - hosted solution but hosting is in the US and we are in the UK and shop will be hosted on a subdomain as a result

This is really bad... I would not do this.

Is it worse for SEO to host your store in a different country or to host in your country but your store potentially run slower?

Door A and Door B are both bad choices in my opinion.  I would go to Door C - higher quality hosting.  Might cost more but Door A and Door B could be so bad that you lose a fortune in sales.