Look basically It's not enough to have simply read a few article pieces featuring murderers and to base your judgement of what is extreme and what isn't by what they write and say. It's like constantly reading articles about Donald Trump and saying "America is a bad country because look Trump wants to ruin the world in its name and so all Americans obviously have the same interpretation of what it means to be American like him". "Where are the moderate white Americans condoning him - no I want a majority not a just a handful of politicians" one might ask. The majority of Americans are living life. Studying at school. Having a job. Raising a family. Their opinions differ to Trump's drastically but their voices aren't the ones featured in the news because the media wants drama and outrage. Featuring a normal person living their normal life isn't glamorous enough to make headlines. And so the above analogy can be applied to the presence of your typical Muslims - they aren't heard so apparently to the new reader they don't exist.
Having true understanding of what Islam is comes with firstly actually picking up a Qur'an and reading it. The whole thing. AND THEN comes analysing and reading up into the tafseer (commentary by esteemed companions of prophet Muhammed at that time, as well as scholars who made it their life's work to extract the true meaning and context of the verses) of the Qur'an and reading up into the fataawa (rulings) of accredited scholars, ones that have authoritative creditentials from a renowned institute, not your "angry sheikh/imam" featured in the daily mail (which most of the time isn't actually true, as with the case of Ali Hammuda - I was actually dying of laughter at the ridiculous conclusion the trashy journalist had drawn from his speech, like I didn't think it was possible to even interpret his words in that way)
Do all Muslims partake it such vigorous scrutiny of the Qur'an and Islamic teachings? Nope. Can they still practice the religion in its true form without compromising basic human decency and morals? Surprise surprise YES they can because firstly islam promotes decent qualities (don't be like "I haven't heard of any verses like that" GO AND READ THEM FOR YOURSELF FROM THE ACTUAL SOURCE (I personally recommend Bayyinah institute on youtube, they have an excellent selection of educated people) and also because Muslims who aren't scholars, when reading the Qur'an on face value acknowledge that they don't know the context of the verses and so don't jump to the conclusion that eg. said verse written specifically for the duration of the Battle of Uhud is a call for Muslims to uphold a continual state of war for all of time, after said battle had been ended by both parties 1400 years ago. And also because if they were they they wouldn't have time to like practice the five pillars of Islam which are the fundamentals of being a muslim (and surprisingly none of which are 'war')
Basically in conclusion the "muslims" featured in the news have reached their conclusions of Islam because they did exactly what you did - form judgements based on a frail and shallow understanding (which thankfully in your case has only led you to have a prejudiced view of Muslims (WHICH BTW I DONT BLAME YOU FOR AT ALL - our governing and media system is to blame for pushing this shallow narrative instead of encouraging people to educate themselves - education is the only true cure to ignorance)) but as we do see on the news, it can have catastrophic effects which hurts both muslims and non muslims.
As I've mentioned before I have muslim cousins and friends so if there's anything more you want clarification with or help, contact me on tumblr (blog is djoudee) and I'll be more than happy to ask them for you.
I sincerely hope you don't take this as me hating on you like I think you are a sensible person but just haven't had the chance to be exposed to the right influences - so stay cool and be open to acknowledging that nobody has a definitively "right" judgement so we should remember that there's always another side of the coin to look into.