Admission for a PhD position in a Sweden university I am a first year BSc student in pure mathematics. I like to continue my PhD studies in Sweden, directly after BSc or otherwise after having MSc. Unfortunately, not only free education for international MSc students has been stopped several years ago but also the living cost in Sweden is very very high. Only leaves PhD studies as a final choice as they pay for tuition fees and living expenditures. 

I have heard that the only way to get a PhD admission (with scholarship) in a some university in Sweden is to do MSc in some Sweden university so that the professors will 'know' you; in other words, contrary to US or Canada, they prefer to know students in their classes than reading about them from the recommendation letters sent from other countries. 

A friend of mine, planted this wishful idea in my mind that if I accomplish (much?) more in my BSc time that PhD students do required for their graduation (i.e. good published papers), along with other things [recommendation letters, GPA, etc] so it may make me more appealing candidate than a person whose professor knows him/her personally. [Q.1] Is this true? And if so, [Q.2] how much 'better' than minimum-required-papers-to-be-published-for-a-PhD-to-be-graduated I need to do? Is there any measure for 'better' papers at all and what are they? 

PS I am sure a person who solves Riemann H, attaining an academic position let alone PhD is trivial; so obviously sky is the limit. I am wondering about the minimum of "impressive results" in research (capability to be a productive researcher) one needs to do for a guaranteed PhD position which should be achievable during 3-4 years time that I have.
You heard wrong. You 1) don't need to know Swedish professors personally to be admitted (although it helps of course), and 2) you don't need to have achieved more than what PhD students need to graduate. About #1, it's the same as elsewhere. If you know the professor personally - and there are ways to do this other than studying in Sweden, you can for example email them or speak to them at conferences - then that's good because they have firsthand knowledge of you. For the same reason if your recommendation letters are written by people who the professor knows personally, that's also helpful. But you don't have to have these personal contacts, and having them doesn't guarantee admission; they're only helpful. As for #2, if it is ever true, you'd be an exceptionally qualified applicant.

Finally about the PS: applicants with a BS degree typically have taken a lot of courses, and have some research experience. That could for example include a final-year project (also known as an Honours project in some places), summer research programs, or various internships. If these leads to published papers then so much the better, although it often does not. What really matters out of these projects is that you've worked directly with a more senior academic who'll become one of your recommendation letter writers. Impress her, and you'll have a much stronger application.