How to win top laning phase?

Hi, I just wrote this post because I really don't know how to win top lane, especially how to win trading in early game. My best roles are jungler and support, I believe over the months I was able to learn how to save my teammates and how to make them kill as many enemy players as they can. I also learned how to carry games with these 2 roles. However, I know a good player has to be good at every role, and I have huge problems with solo lanes. I had to realise I'm a terrible top laner, and even a worse mid laner. I don't really enjoy mid, so I decided to learn top because this is a lane I consider to be really interesting and the other people said it would be easy to learn. When I started getting known with the lane the followin thing happened: The minion wave has arrived, we started farming. We were lasthitting pacefully ( he hit lvl 2 first), and when i reached the same level as he I saw an opportunity and attacked him. What I noticed was that his abilities did much more damage on me than mines, suddenly i got low hp and had to flash to escape with my life. I don't understand how it's possible. I had the proper runes, masteries, and starting items. Well, I drank some health potions and came back, but the same thing happened. The enemy got ahead at farming, was at a higher level already, and he started harassing me... He didn't let me farm, whenever i went forward to lasthit he attacked me. I asked my jungler to help, he did it, and the enemy felt back. But I was unable to farm enough to get as strong as him, he came back and everything started over. I couldn't farm effectively enough under my turret, and after like 10 he was able to dive and kill me with his jungler. I got completely destroyed, but when I needed to teleport on the other side of the map, I was able to help my teammates to get some kills. Actually I did it quite well at teamfights, but then the enemy top laner tped too(who was higher by 2-3 levels and 1-2 items) and we got killed again. Of course my teammates started raging at me for feeding the enemy, and I was really sad because I knew they were right.

To make it a bit easier to understand, I'll describe some exact situations where I lost my lane: 1, I played Rek'sai against Nasus (I had no better top lane champs, and I saw pro junglers using jg champs on top successfully) I decied to play passively and tried to farm under my turret, since top was new for me then. I waited til he wastes all his mana killing minions but he didn't do it. He used only his q to lasthit (he lasthit almost perfectly) and never used his w. Before tping back I decided to start a trade. I knocked him up with W and then began to AA him with Q, but he took almost no damage! Then first he hit me with Q (it took like 1/5 of my hp) and then used that W+E combo, and I got a ton of damage. I teleported home, but when I came back Nasus did the same, harassed me, I couldn't farm, and in late our whole team got destroyed by him. Anyways his jungler tried to help him several times, but I always managed to escape with W+E.

2, I played Nasus against Pantheon When the game began he must have been afk or must have wasted too much time giving a leash to his jungler Gragas. I've already reached level 3 when he arrived so I made him fall back easily. Even at level 1 he was able to deal more damage then me, but since I had 3 abilites I was able to win the trade, I didn't let him farm and chased him towards his turret. But then I made an enormous mistake: I was farming under his turret and forgot to ward the bush. Suddenly a full hp lv 2 Gragas attacked me, and the lv 2 Pantheon was able to pick up the kill. I teleported back immediately, but then he was already lvl 3 with approximately 3 times higher damage then me( with starting items). He didn't harassed me, and I had more cs than that guy all the time, but that was only because he kept teleporting all around the map and killed my teammates. I decided to splitpush instead and destroyed 2 of his turrets. However in the end of laning phase he had 8 kills and 1 dead(!). I know it was a mistake from me at that point, but I learned from that.

3, I played Vladimir against Cho'gath (this happened today) The game started well, he was much ahead at farming but I was able to kill him by a successfull gank. But then he tped back got behind me and attacked me from a bush when i was at low hp. I died, but then tped back to do the same as he did to me. Guess what happened... He had much higher damage on me, made me fall back, and started harassing me. My reaction time wasn't good enough to use my W quickly and avoid getting knocked up, then he used W, then E, and I had to home. After reaching level 6 he was able to dive and kill me without losing too much health. I often teleported to my teammates to help at teamfights as much as i can, and i was able to get some assists, but then that guy came, and hunted us down one by one in the unwarded jungle.

So that's all I thought was important to post, all in all I like this role, but if all I can do is feeding then I can't enjoy it all. Maybe the main problem is that I don't know well enough the strenghts and weaknesses of the champions. I've already tried practicing 1v1 at custom games. I played against some gold and platinum players, they beat me easily, and i played against some silver and higher bronze players. Some of them defeated me, some of them was defeated by me. If any of you guys could give me some advices, I'd be thankful for that.