Horizontal/Parabolic Projectil Movement and Jump for 2D //HELP!

Hi everybody.

Im currently making an adventure game. I have a little physics issue. I have 2 situations:

1- I need to know how do I for shoot or make my character get a horizontal force that Impulses him. I mean.

The thing is, when I use lsd.AddForce(transform.right*500); He moves just a little bit as the dark red cross shows. What I need is my char get impulse as the green mark. Just image if you were shooted by a bazzoca... or if you have something in you back that applys you a horizontal force. Sorry if I'm not explaianing well.

And my second case y very very similar to first one.

Now when I stand on the green box, my char must been affected by the parabolic projectile effect. Note that, it have its own rigidbody, and that one is the have to be affected.

Once I stand in box green I fully jump to the aire, but I never get the parabolic effect, I just move a bit to the horizontal side. Veeeeeeeery similar to the case 1. I'd say, it have to be the same problem. So guys, I will really appreciate who helps me to resolve this. I know my english suck. Thank you so much.