Strong picks against current popular champs?

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Well, yeah, obviously, being tower dived isn't fun. However, it was mostly about the Learning new things part ; Of course, Riven can turn dives into kills with her stun depending of the champion. Same goes for jax... I've done it with a few champions, actually. However, some can't ; Gangplank would be a prime example (Well, unless you outrun your ennemy who eats the tower's shots, but...)

And Azir. Gangplank has his escape through running after using an Ult on the turret or just Q on who you want to eat the most. I just don't like Gangplank as a champion though.

I've read some places that he was amongst the hardest - maybe not to play per se, but to do good I think. Or, well, to do like your average mid laner... Well, if anything, I know I can't play talon like my other mids.

I mean. We aren't Platinum. People won't reliably put down Pinks or Upgraded wards below Gold (unless Shaco comes in the game, then it's like everyone learns how to for that game just from fear). This makes Talons ult easier. Using his ult correctly in a teamfight also takes some practice, but overall -- he's somewhat binary. Eliminate carry in 1.5 seconds, deal damage through ult to enemy team. Laning - manage resources, mana, no overextending, basics.

Yeah, well, the main issue's in teamfights, not lane. Harder to do that when you also have to keep track of his whole team, where he can just ult once he's low and be full... Otherwise,

This is what makes a good player. Keeping track of the entire teamfight. It is also, in my opinion, why the very good Kassadins are the scariest thing ever. Their engage and disengage in a teamfight is just so precise because they keep tabs on everything in the teamfight and know when to do what on who. Same for Zed right now in the tank meta.

The main issues I have during laning is her absurd damage and invulnerability. After she dashes to me twice, I usually feel like I don't have enough hp to fight her and even less damage to duel her. At that point i'm just sitting at my turret waiting for ganks (that sometimes never come) and then she'll ult me and snowball harder than before...

She has insane base attack, but after she uses Q once, you can go to bushes and make her either chase you, or go back to minions. If she chases you, you have an advantage already. Either juke it so when your jungler comes, she puts herself in a bad spot and gets ganked (make sure you tell your jungler when), OR see if you can win the trade from the advantage.

What's your definition of "Carrying in teamfights"? If my team is behind, I can't seem to do much as nunu.. Neither with p. much anyone, actually.

You can't carry in teamfights with teammates that don't deal damage unless you're the one that deals it all (i.e. Riven, Jax, Caitlyn using team as meatshields, etc.); But if they deal decent or more damage, then eliminating the ADC/APC with CC and damage is the start of carrying it. Whether you are a Tank or an Assassin. Also, keeping them off of your carry and hitting CC on them in order of priority is good while keeping track of what CC they have used and capitalizing on it. Nunu is pure objective control and counterjungling. His ult is best used by baiting teamfights or just 2 members of their team into or near bushes (feign running) where Nunu is charging a full ult for them (since it is invisible to them). Massive damage and it makes the teamfight easier (5v3). You can also Nunu ult in the middle of them of course, but that's risky. Blood Boil your ADC, Cube their carry, etc.

Lately, Nunu (Jungle), cho'gath (mid, I'm not sure anymore though since that time the off-meta AD varus mid dominated me) As for top... Keep switching, can't seem to do well - Either keep getting countered or just not doing well. I like gangplank (Hence the big issues with fiora)

Cho mid is still good. For mid I would say Ahri and Annie like everyone else -- but Vlad (also a very strong carry in late game both solo and team), Talon, Cho, Heimer, Swain, Ziggs and Cassiopeia are also good picks. Katarina in lower ELO as well.

Top I believe Wukong, Irelia, Riven, Trynd, Hecarim, Rumble and Vlad are in season. Nasus is shaky but a god if they don't focus you early.

Alongside malphite, I was thinking of getting pantheon and maybe yorick (all for top, jg or both). What's your thought on that?

Pantheon is pretty nice and doubles as a good jungler; Malphite is quite strong at the moment. I have no clue on Yorick other than he counters Fiora. Sort of a champion that just isn't played much. And Rito hates Yoricks coding which is why he's never on free week.