Welding woes...frustrating!!

You are fighting an uphill battle trying to work with the welder you have. As others have said there is a definite difference in what equipment you set yourself up with. I have also found the Harbor Freight wire can be hit or miss on the quality. I have had many customers come in with better welders but using cheap wire. Switching the wire helps. Fluxcore is very particular about the stick out of the wire ( the distance between tip and metal) You want to bring it in close enough that the crack and pop becomes very consistent in sound.
Also the duty cycle will not effect the quality of the weld as in dropping off. It will shut off the drive motor when you exceed it. A consistent drop off of the output while you are running longer welds gets into one thing- voltage drop off. Whether it is the incoming voltage due to a poor extension cord or a loose connection where the cable connects to the ground clamp (run into this alot) or a bad /weak ground clamp. As the weld time increases the connection gets worse due to heat which causes your output to drop off.
An inexpensive but decently made 110v mig welder is the Eastwood one. I think it runs under $400. The only part of it I don't care for is the drive roll setup but it is consistent now to what Lincoln and Miller are putting in their welders now.