No. Even the lamps don't work.
you get agility exp and when you lvl up, you can run longer
Yes.
No you cannot as agility training is only a member skill so it is put in member places so on a free world you cannot access the member areas so the answer to your question is no.
It temporarily increases your agility.
The brimhaven Agility Arena.
As a member in Runescape, you get lots of new skills. Agility, Construction, Herblore, Summoning, Farming, Thieving, Fletching and Slayer. And you get lots of improvement to the skills that f2p can acess. It is all about which skill you like more. If you want a skillcape, i recommend Fletching in member skills.
You keep your skills, but you can't use them.
Go to the course closest to your level. If you are level 1 go to the gnome course!
this is not possible unless you cheat. plus you need membership to get agility
There are a number of online sites which contain free RuneScape agility guides. The web domains "JBastow.HubPages" and "Tip.It," for example, contain these guides.
It may involve agility.
Really depends on what skill. For mining, agility, and firemaking, you want a penance horn for double xp.