ARAM basically teaches you to dodge skillshots. It's literally dodging simulator since you have 5 champion abilities to dodge instead of 1 or 2. That's where I learned it basically though you can learn it from stuff like Urf as well.
Pathing depends on what you are doing.
If you mean pathing as a jungler, it's something you learn I guess. Look at the lanes and you'll see that X person is over extended, so if you are on that side of the map maybe hover nearby incase they get ganked if you have camps available to clear. Or you see that the enemy is pushing hard, so you can try to gank to relieve some pressure from your laner.
If you mean pathing as a laner, the safe path is generally the best if you don't have vision of the enemies. Why walk through river when walking through your jungle is safer 90% of the time? It kinda depends what you are playing though, because if you are the tank for your team, then you need to be the first one to investigate that bush if no one else can. But, more often than not you just want to be safe.
Itemization depends on a lot of things.
Mostly just look at who is a threat and what role you are. As a support main, i play a lot of enchanter supports who die if hit by anything. So me building Merc treads isn't going to save me if I get hit by CC. However, as a Darius who wants to be in a team killing, Mercs make a huge difference if he's hit with CC. As a squishy champ, look at the threats. Are they mostly AP or AD? Can I dodge damage easily like using Zhonya's to avoid Syndra's R damage or Zed R? Or is it a LB or Eve who will do half your health bar out of no where, then maybe hexdrinker is best. If they have someone who heals, just buy healing cut regardless. There are very few champions who don't have/use heals so buying healing cut is a pretty safe choice in most games since the ADC will probably buy lifesteal later anyway.
Looking at the minimap is something you just have to learn. People recommend setting a timer that plays a sound every few seconds and looking when you hear that sound.
Playing around cooldowns is something I learned when I was playing bots.
Walk forward slightly and the bot will use X spell, so you walk up and back over and over until they use that spell, then you wait/dodge and then fight them afterwards while it's down. Against bots is really easy to beat them because they just use abilities aggressively it seems, so once it's down you know you can fight.
Mostly you just need to think about what will lead to you dying or what is that person maxing. Getting hit by CC is always bad, regardless of the damage from that ability because it is generally the set up for more damage, so avoiding CC should be your main goal at all points. Maxed abilities are secondary. Lux's E does a ton of damage since she maxes it, so dodging that is important, but it's better to get hit by her E than her Q as her Q will likely lead to her ulting you.
It really depends on how much you play. Also, try watching people who teach League like Foxdrop, Anklespakin, or SoloRenektonOnly. They try to explain their point of view so perhaps hearing someone explain their thoughts will help you understand why they made the choices they made. There are probably other teachers out there but these are the big ones I've heard.