Off course! More Backlinks means solid strength of your website! It also benefits website to obtain many positives from various SEO aspects
The Statement need to be bit more modified. It can be said ,'More back links from quality sites ,the more better, more backlinks from bad link neighborhood can ban your site even'
Of course! You just said that. Anyway, it's really important for SEO purposes to gain organic traffic from SERPs. Good luck!