Inquisitive, unfortunately being part of the Torah world doesn’t mean we’re impervious to bad middos, or even abuse. Being ehrlich in one’s middos is a lifelong endeavor, and some people might think that they are doing just fine without it… It’s very sad. With or without the externals, we’re all going to have these challenges. It’s up to us to take every opportunity possible to improve on those issues and identify the middos that we have and how to fix them.
That being said, the outside world is full of lashon hora and bad middos, not to mention untznius things – it’s how non Jews enjoy themselves. Most comedy is about making fun of someone else. Being part of the outside world definitely doesn’t help you grow in middos… Just imagine how much worse your parents would have been if they spent hours learning bad middos from movies and television…
Hashem says “i have separated you from among the nations to be mine”, and chazal say on that pasuk…if you are separate from the non jews, then you are my people – the non jewish world is not all bad; we benefit from science, medicine, buildings and the economy, but the culture is anti Torah and only exacerbates the challenges we have from the yatzer hora on a daily basis.
As to your questions in halacha; many poskim hold that one is not obligated to wear a hat and jacket while davening if that’s not how he normally dresses when meeting someone important. That just means it’s not an aveirah; we know that there’s a lot more to yiddishkeit than just “do this” and “don’t do this”. A hat and jacket is a constant reminder to a ben torah that he is part of the “ligyon shel melech”, the legion of Hashem – when it comes off, that feeling is partially lost.
A vartel is a different story with two opinions going back hundreds of years. Chassidim hold like the poskim who say it’s an obligation, and most litvishe hold it isn’t.