Nope just kill Black Dragons, King Black dragon, Iron Dragons, Steel Dragons, Mithril Dragons. My first visage was at 726 Iron dragon kills, then I got another one on a Iron Dragon task after 28 kills. You can get some great drops by killing them ranging from 200k-38m.
No you dont need to complete dragon slayer to get one but all vissage drops are extremely rare like 1000 in 20000 rate.
No, membership is not needed to get Dragon Slayer Class.
You can either obtain dragon boots from other players via trade, or grand exchange. Or you can kill Spiritual Mages who drop them quite often. You need 83 slayer to kill them.
There is no doom slayer. you need to buy it
If you drop the map pieces, you will need to obtain them the exact same way you did before, the hard way.
go to runehq.com they have everything you will need for runescape
If your talking about the Dragon Slayer in Adventure Quest then it's called Guardian and yes you do. Scholar and Fighter both have to reach level 10 before you can exceed in the Dragon Slayer Class. As a Normal User your Class can only reach 5 MAX.
If you want to, u need to beat the red dragon 8 times. answer from DrakoFighter
you need to get 5 undead slayer badges
If you look at the Dragon Slayer quest in your quests tab, it should tell you all the recommendations that you will need, if it doesn't or they are lined out - it means that you are ready to start the quest.
You just fight him, and have a good amount of food on you. You will need a dragonfire shield. That's about it.
Given that Runescape itself is a browser game, yes.