"széles e világon" is a phrase, literally meaning "on this wide world". "e" is a short / kinda artistic way to point at something and say "this". Other variants of "this": "ez" / "eme" / "ezen". Basically the sentencem eans that this adult (weird choice of word there, really) is your best frend among all the humans living on this planet. "széles" is "wide", "világ" is "world".
"ilyesfolymán" in the following sentence is just a fancy way to replace "tehát" ("so"). This must be some sort of business term preferred by people nowdays who want to use super long words in their letters on order to create the feeling that they are highly educated. Originally it means "more or less like that", and as far as i'm concerned there isn't much difference between thew two words, you may use them interchangeably.
But honestly, I'm 29, I had my fair share of education too, and I am fairly certain that I never ever used any of those two words in my whole life. I also asked the person sitting in the next room, and he had no clue what could be the exact definition of word, he only managed to come up with a more-or-less accurate description.
My point is in theory you could get a C1 level certificate in Hungarian and live a long and fulfilling life in this country without using "ilyesformán" once. :)