Please find my response below:
1) Check my API usage? I went to the link and beside the Translate it says "Pricing • Courtesy limit: 0 characters/day"
Please do not tell me you need to pay additional for the service of translation on Google??
-- You can pay, but I think that you don't want
Currently Google is making their API commercial and not all the clients get a free courtesy limit.
2) For some reason the /fr translation started to kick in, just after you visited the site. I could see you via woopra. But it only translates the home page, not when I navigateand /FR is the only translation that works. /es /sv etc do not work, only English.
After you use the suggested # gtranslate config block instead it will work.
3) Use Google without the API - Can you explain why I would do this and is there a disadvantage?
There is a disadvantage. API is stable which will not change without notification. If you don't use API, Google can change their coding standards and in that case you need to make appropriate upgrade to continue getting new translations.
So if you want 100% stability, you better pay Google or use Bing Translator instead.
4) As per point 3, can you let me know if all that text goes into the htaccess file?
Yes, you need to use it instead of # gtranslate config block you already have.
5) thanks for pointing out the sitemap.txt, my bad. Note: I already I have a sitemap.xml and a gzipped one. I assume it is fine also having a sitemap.txt there too?
Sure, you can have more than 1 sitemap.