A/C condensate draining line under sink - need help

Hi all! I replaced the countertops, sinks, and faucets and currently working on the plumbing underneath the sink. I have an A/C condensate drain line that leads into the plumbing underneath the bathroom sink. I don't have any plumbing experience but I've done some research and everything is going well so far.
The only problem I'm having is that I'm not finding much info on the subject of replacing that drain hose. It's a thick black hose, and it has some type of clay(it looks like hardnened plumber's putty) which is holding the ends respectively to what it's attached to, which gives it a good seal and prevents water from leaking out.
My questions are:
1. What is that hose called and where may I purchase some
2. What type of clay is that and how should I apply it?

Ultimately, I'm just trying to figure out the steps needed in order to replace that drain hose. Thanks so much for your time!!

P.S : I know that the P trap is backwards. That's why I'm replacing the plumbing from the previous owner. Thanks!

7/8" dishwasher drain hose.
Forget the clay.

flip the p-trap arounf
The branch tail piece is below the trap arm going into the wall.
The 3/4" branch needs to be above the drain going into the wall.

Look for a 1 -1/4" threaded branch tail piece. The closer the branch to the threads ( higher) the better.
It will screw into the bottom of most brass pop-up assemblies.
This should get you above the drain to wall.

Thought I had a thread on something similar.

I'll start a new one and link it here when I am done.

AC Condensate drain defies gravity

Hose you can get at any hardware store or big box store like HD

this one @ HD
Sioux Chief 1-1/4 in. x 7/8 in. x 2 ft. Rubber Disposal Hose

some times it can be really hard to push onto a 3/4 pvc pipe.
A little liquid dish soap will help lubricate it.

How do I even pull this hose out of the wall?! It won't budge

Take off the hose clamp . Slice the hose lengthwise.
It most likely 3/4 pvc sticking out of th wall