Hello Shannen, Welcome back to Argonath (Although i never saw you before :razz:)
Answers to your questions (In Order):
1- Download the LAST version of the
Client Installer at the pages Omri Said, Install it, Follow the instructions, And there you are. PS: Go to San Andreas Folder and find the SAMP Laucher, And make a shortcut from it to Desktop (To launch it easier)
2- Nothing, Just client installer, Look #1 and Omri's post

3- You mean, Custom Objects and Scenarios that are not on the Original SA Single Player? Well, Due to this question I can guess you were a MTA VC Player, Well, SAMP Counts with a Map Editor downloadable from the SAMP Forums, That allows you to create your Custom Scenarios for your server

, But Dont worry, You do not need to download it, Unless you plan to make your own server

, The ones who need the map editor are the Argonath Developers :P
4- About Lag, It depends on your connection, You can read the other topics in this board about to fix lag...
5- About System Requirements, You just need the San Andreas game installed on your PC
VERSION 1.0, Not V1.1 OR 2.0 and a Fast Internet connection

, and ofc, 5.6 MB Free space on Hard Disk...
"How to know the Version of my SA?": Run the game itself, and then look at the bottom right corner, If it does not say anything, Then its 1.0, Otherwise should display "1.1" or "2.0"
After Installing, Open the client, and add this IP: 89.149.196.238:7777 to the Favorites, Click "Connect" and Voila!