Re: Japan
The claims about Japan/Islam are largely urban legends.
There aren't very many Muslims in Japan because the numbers of ethnic minorities are lower than most countries and most minorities are of Chinese, Brazilian, Philippine etc. heritage.
However, Muslims can get PR and Japanese citizenship here. No rules against this, nor are there any rules against propagating Islam, importing Qurans or anything else, really. And Japan is recently working to boost its tourism trade, so in fact there has actually been some official sponsorship of welcoming Muslim visitors and encouraging restaurants to develop halal options for Muslims visitors, developing advice services so that Muslims tourists can find a local mosque and so on.
And as for universities.... recently, an extremist preacher Dr Zakir Naik gave a lecture at Tokyo University (during which the audience was segregated by gender--even though this is against the law for a Japanese public university). No particular reaction to any of this. Nor are there any restrictions on Islam at Japanese universities in general.
Japan has experienced a significant increase in asylum seekers in recent years, very many of whom are Muslim (however, the absolute numbers are still fairly small by European standards). Japan grants residency rights to very very few of these. However, the majority who are rejected do not actually leave Japan, but tend to give the authorities the slip and go underground, working in the gray economy, gravitating around particular areas like Ota in Gunma Prefecture. Subaru and other Japanese companies in cities facing labor shortages hire some of them--via labor brokers, so that they are not technically breaking the law. Most of these ASs are no doubt harmless enough, although there have been some worrying hints of extremism in some of these pockets.
I doubt that Japan will start to accept larger numbers of asylum seekers, as they had a rather dodgy experience last time they tried doing this, back in the late 1980s/early 1990s with Iranian refugees.