Because you changed the derailer and went to 7 speed, I'd try the cheap/no cost fixes first. Have you checked the derailer to be sure the stop is set correctly for the high gear? When you went from 6 to 7 speed, did you check to see that your rear wheel is dished correctly? Have you checked chain wear using a one foot ruler using the method described by Sheldon Brown?
If the chain is good, and all the settings are correct, you might want to take sam83's recommendation and go back to the previous 6 speed freewheel cause the 7 speed may be worn.
As for the index shifting, you didn't say which shifter brand you have that has 7 speeds. Suntour 7 speed from that vintage is not interchangable with Shimano 7 speed. The freewheel spacing between the cogs is different and the pull by the shifters is different. So if you've got a 7 speed SHimano freewheel and you want index shifting, you need to have 7 speed Shimano shifters.