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Logo: would lose the star and the reversed 'R' at the end. Not sure about the asterisk in the brand name: it creates an inconsistency between the domain name and the brand name.
Would put more products on homepage. Special Offers too and something like Free Delivery if you can - Free helps sell.
Make the grey text darker for readability - contrast is your friend.
Emphasise the prices more, much more.
Put in a proper contact page which includes the postal address - important for trust. Don't bury the address in the T+C and FAQ pages.
Do more SEO especially on the keywords razor blades.
I kind of like/understand the use of the reversed R, it's meant to look Cyrillic.
Besides that, your current homepage is not suitable for an e-commerce site - http://razwarie.myshopify.com/collections/all needs to be the site homepage (but with fewer products). It's a nice design, is it a standard shopify theme or did you customise it?
I find the name a bit clumsy, as it's not obvious on how it should be pronounced - this makes it harder to remember and harder to communicate. As Tricky said, the logo doesn't help matters much either with the asterix.
It'd be good to have a Facebook Like box on the homepage to give the product more public endorsement. You can use this as well to do promotions/competitions etc.
If people are to try out your product they'll need to know why it's different and better to the popular brands. There's nothing to communicate its best qualities on the home page.
Your showcased product says "Women only"...the branding looks like it's definitely targeted towards guys so this seems a bit odd.
Finally, if I were buying a new razor I'd want to know how easy it'd be to get blades later on for it. ie is it compatible with any regular brands etc.
