>What did go wrong to the point of japan closing itself to the world? Were Ieyasu and Hideyoshi (and the other shoguns) possessed?
I'm not sure I'd go as far as "possessed" but they did not like foreign influence, especially when it brought something as strange as Christianity to them. A lot of Japanese at that time (and even many today) saw Buddhism as an intolerable foreign import, the same way a lot of European nationalists view Christianity itself (i.e. a non-native, destructive import which is hostile to their folkways).
It was for the same reason that the Japanese later on in the Meiji era actually made Western powers engage them on their own terms with the Equality Treaties rather than being treated like China and India.
>How responsible were the dutch and the english for the anti-catholicism there?
The fact that it got to the point that only the Dutch were able to stick around in Japan during the Sakoku era (albeit tenuously in Dejima which because a foreign port town, the only place westerners could visit) is pretty telling. They didn't cause it, but they clearly had no fellow feeling with Papists and didn't mind sending countless Japanese souls to Hell on principle if it meant they could make money.
Also https://en.wikipedia.org/wiki/Rangaku
>Was the sentiment of japanese culture being replaced by that of the west inevitable? Would it have been possible for the missionaries to preach christianity without carrying western tradition?
This is a kind of loaded question since it assumes Christianity is something exclusive to the West when in fact it is universal. Many of the mores and customs of Japan (homosexuality, suicide-culture, pornography, lewd theatrics, paganism etc.) would have had to change, not because they are "Oriental" but because they are sinful and degrading.
Christianity itself has a really remarkable knack for making other cultures conform to it without losing uniqueness though. It's only when you try to change the faith to fit the world you see the decay start to creep in.
I think the most "Western" thing about it would be the use of Latin, which might be a problem for Japanese speakers, to the point that they may have been given an indult to say mass in their own language. That said, under Orthodoxy this might not have been an issue.
>How could the orthodox have changed that timeline?
Probably not, since at the time this was all going on arguably the most powerful Orthodox nation, Russia, was still making its way across Sibera, and was nowhere near the Pacific until the end of the 17th Century.
>As for christianity before the missions, one can only wonder the impact of nestorianism there.
This took a really big hold on China for quite a few centuries, and in other places along the Silk Road. It wasn't as successful as Islam was in these places, but in China they established whole sees and I think in the Tang dynasty a lot of courtiers (possibly some emperors too) were Nestorians.