2012 Dong Fang SX-R. Name this part?! Top speed 50 mph?! Sputtering after 30 minutes

Hi everyone! I was wondering if anyone could help me solve some issues with my 2012 dong fang sx-r 250cc. I have Googled my bike's symptoms over and over and have been reading and working on it for 2 weeks now. I'm trying to attain safe highway speed and have a healthy bike.

When I bought it, it did not spew oil everywhere, but when I changed the oil and put 2 and a half quarts in, I went for a short 5 minute ride yesterday and did not notice until this morning that my bike looks like it projectile vomited everywhere and there is oil all over the bike and ground. The oil came from a part that I am not able to name. Sitting on the bike, the part is on the right hand side connected to the crank case. It is a rubber pipe connecting the crankcase to a small cylinder peice that has another rubber pipe on top that it not connected to anything and there is no clear spot to connect the peice. Can anyone tell me what this part is and what it is suppose to connect to?

My other issue is my top speed. My odometer is reading incorrect and I know this because while it says I'm going 70mph in 5th with throttle fully open, I had a friend in the car next to me tell me I'm only going 50 as semi trucks are passing us up on the freeway. I've Googled what could be the issue and have tried:

1-Cleaned the carburetor both by taking it off and putting carburetor cleaner in the gas tank.
2-Checked for blockage in air filter assembly.
3-Changed fuel and air levels in carburetor to put rpms at 1500 so it will idle.
4-Checked all of my electrical connections.
5-Changed, low and black, oil from 10w-20 synthetic to 20w-50 valvoline racing oil. On the short ride I tried seeing my top speed and odometer read 60, but I barely felt as if I was going 35-40.
6-Changed incorrect and burnt out spark plug to npk iridium that is meant for the bike.

My third issue, which may be solved with the spark plug change and oil change since the plug was bad and oil was low. But just to be sure no one has any other ideas. When I either ride on the freeway for about 5 miles (5th gear throttle fully open, which I know is bad but I was testing speed) or ride surface streets for around 30 minutes or more, my bike sputters really badly when accelerating and at high rpms, failing to reach 30 mph. When I pull the clutch in and brake at a red light, it dies. After that happened on three separate occasions, I checked the spark plug and it was done for so I changed it. It happened again the next day so I checked oil and saw it needed to be changed. All of this happened after cleaning carburetor by taking it off and riding with cleaner in gas tank trying to fix top speed issue.

This is worth mentioning, I am unable to idle at 1000 rpms and bike shuts off when I close the choke after bike is warmed up or even after I've been riding a bit. So my idle is set at 1500 and I ride choke half open.

Not sure what else to put, but iwould definitely be grateful if anyone is able to help me out. I don't have money for a mechanic or anything pricey.