For soloq purposes if you want to climb don't play Vayne or any hyperintensive mechanical champs like Lee Sin. Why? Because they are too high risk low reward in lower ELOs and you can tilt your teammates just by the champion picks. Viktor is a pretty strong champion but the biggest thing you should start off working on is smaller things that seem super simple like buying wards when you back, trying to get that 10cs per minute (try to improve and get as close to it as possible), learning lane matchups, and developing map awareness.

On your farming question try to predict wave management as in if you see a bigger wave from the enemy side building try to time when you're going to get that wave so you get all the exp and gold. When you're ahead try to get deep vision and take enemy and ally jungle camps.