Hreflang is used at a page level, not at a site level. So no, you should not just set the hreflang tag on every page of www.mywebsite.com to read:
So yes, if the German translation of the page www.mywebsite.com/page.html is available at www.mywebsite.de/page.html then you must do 2 things:
1. On www.mywebsite.com/page.html use <link rel='alternate' hreflang='de' href='http: mywebsite.de="" page.html'="">and <link rel='alternate' hreflang='en' href='http: mywebsite.com="" page.html'=""></link rel='alternate' hreflang='en' href='http:></link rel='alternate' hreflang='de' href='http:>
2. On www.mywebsite.de/page.html <link rel='alternate' hreflang='en' href='http: mywebsite.com="" page.html'="">and <link rel='alternate' hreflang='de' href='http: mywebsite.de="" page.html'=""> </link rel='alternate' hreflang='de' href='http:></link rel='alternate' hreflang='en' href='http:>
What this means is that the English page should link to itself and to all other language variants. And there should be "return tags", i.e. each of the language variations should link to themselves and to all other language variants.