I am not a fan of Mobility Boots in a final build because I consider them good only early-mid game when you want to run around and create pressure / help your team. In late game, there are much better boots such as: Mercury's Treads or Ninja Tabi.
Sunfire Aegis is a ****ty item: while it is good early - mid game because it is fairly cheap, in late game a Randuin's Omen is just better. Don't keep it: if you really need an item like it buy a second Randuin's Omen because it just gives higher stats and the 40~ damage Sunfire Aegis deals just won't be observed by anybody that late in the game.
I also think you should talk about your abilities more instead of copy pasting from lol wikia. I am not a fan of maxing Sonic Wave(even less if you are a begginer) because if you start a gank with it and miss it, you are done. Maxing Tempest / Cripple is just safer to max because you can just walk up to your enemy and Cripple him(or ward hop to him for that matter) and keep Sonic Wave unused till you are sure you can land it.

I feel like the guide needs more depth but it's a good start.
Not sure I agree with the Spirit Visage being built instead of Banshees most of the time after the nerf to SV.

Jungle item should deffinately be the first item and sightstone after.
Sunfire cape and spirit visage or both situational items. Maw of malmortius
and randuins omen are both doing the same purpose but better.

It's just a general guide

Way more information is needed, though the title is really good ;)

You can't max a spell by level 8

I was going to do that because I noticed it right now,thank you.

You forgot to close your columns in your spells chapter.

[columns]
[nextcol width=100]
[center]
[color=#ffff00][b]Tempest[/b][/color]
[icon=tempest size=60][/center]
[nextcol width=30]
[nextcol]
[[Lee sin]] smashes the ground, dealing magic damage to all nearby enemies and granting true sight of them for 4 seconds. If [[Tempest]] hits an enemy, Lee Sin can cast [[Cripple]] within the next 3 seconds.
[/columns]

Same for pros & cons, you got some nesting over there. Use [/columns] after every column sequence.

Also, it's Flurry, not furry.

Best of luck,

Foxy