Since the only problems cames from my Tourney rear derailleur. I want to change it to a Shimano Sora derailleur, but, I don't want to change the shifter, I'm ok with 7. Would a Sora rear derailleur work with a Tourney 7 speed shifter?
Yes, despite being from a 9 speed road groupset it will theoretically work. If fact any Shimano road or MTB shifter for 9 speeds or below would theoretically work. The reason is that for 9 speed and below derailleurs, Shimano used the same cable actuation ratio - the ratio of cable length pulled to cage movement.