Hey there,
the reason for ranking in different countries for the same keyword could be fact that it's very similar in all the affected languages. I don't know which KW's and languages do you exactly mean but let's say for example _"tennis, casino, mobile, video, dinosaur, coffee, tea,..." _are very similar throughout the countries.
Also, the reason for higher rankings of the log-in page could be poor optimization of the internal linking. Maybe you have more links to the log-in page, maybe the links have more relevant anchor texts or maybe your homepage has bad UX metrics compared to the log-in page (people usually go to this page to complete the action which means very low bounce rate).
More information regarding the KW's and countries would be appreciated. Cheers, Martin