I read many times the expression くそかわ referred to babies, what does it exactly mean in english?
I know that くそ means "damn" while かわ comes from かわいい, right?
So damn cute?
Yes, right. くそ・クソ・糞 is used in place here for what usually would be すごく, e.g.
(As slang is usually more versatile, there are more expressions with クソ, where すごく isn't a valid substition, e.g. 糞美人. Also, note that くそ isn't traditionally a positive interjection/prefix/..., but traditionally used to embellish derogatory terms.)
I'm not 100% on the precise ordering, but クソ is probably the most recent of a series of similar expressions
In any case, as you guessed, it is a stronger expression, just as in English:
As you say, かわ is just a short form of かわいい, as common with all "i-adjectives", うまい => うま(っ), すごい => すご etc.
It means F**king cute.
It is commonly used by gals, but it can be a little rude so I will not recommend you to use it in public.
It is one of the gal language - for more informations on gal language visit http://injapan.gaijinpot.com/featured-photo/2011/09/14/japanese-gal-language-what-is-%E2%80%9Cagepoyo%E2%80%9D/