Corrections/suggestions for a more natural flow:

Honesty is a very good quality. We all want to work with and to be friends with an honest people. But do you think it is possible these days? Specifically in business or [school]?*
I was just talking to my friends, and we had different opinions about that, so I want to hear your point of view.
Is it possible to be honest in this world?

*In written English, you don't typically use ellipses to trail off a half-finished thought in this way. It would make more sense to follow the ellipses with a question mark: i.e. "Specifically in business...?" rather than including the "or."

I tend to offend people because I actually honestly answer the questions that they ask.  I used to play in a concert band.   There was a lady close by me in the saxophone section.  She was truly a bad player.  Once she asked me, "I'm not really that bad of a player, am I?"  I kind of just looked down at the floor with a pained expression on my face and didn't say anything.

She was not happy.

Then there was the lady who sang a solo in church.  Really she should not have been singing a solo in church.  She couldn't sing very well.  Afterward, she asked me, "What did you think of my solo?"

What I actually said:   That was very...melodic.

What I actually wanted to say:  For your sake, I hope that God is as long-suffering as you say He is.

I have a couple of friends who routinely lie.  This annoys me because I never know if any particular thing they are telling me at the moment is true or not.  One of these friends, when I first met him, said to me, "I'm trying to be more honest."  So now I never know what exactly is true.  

I knew a girl in college who seemed to have a life that was so uneventful that she would make up exciting things that happened to her.  She had moved away, and my friend called her up to see how she was doing.  "I've been impregnated by "so-and-so" (a famous movie star), she announced.  Two weeks later, my friend called her again.

"So, Lori, how is your pregnancy going?"

She hesitated for a minute, and then casually replied,  "Uhh...it died."