Why does the first one use と and the second and third one use ように?
My understanding of these sentences is:
1) When learning Japanese it is thought to be good to avoid using romaji. (the meaning is that it helps not using romaji, making an effort to use kanji or Katakana instead);
2) The future of Japan is thought to be dark.
3) He is thought to be rich./It seems like he is thought to be rich
In the first one と is more direct, while using ように思われる is a softer way to express an opinion (it seems like). I don't think it reflects much in the English translation.