After the download I do not think so, once lauched once and a new profile created you can play without an internet connection.
Use a memory stick.
N it doesn't use Internet
No it does not have to but it it is recommended!
You can't it will just appear as a normal picture.
I use Google Chrome instead of Safari and there are no issues with downloads. I am not familiar with Safari Download Manager.
use your internet download manager.
USE Internet Download Manager For downloading files\ AND Vuze for downloading torrents
The best deal on an internet download manager is CNET download. This is good because they are commonly used among many people and is an easy to use server.
If you have wired on wireless you need to set it up which is really easy using the setup manager which is under Settings or System >Internet settings. When you have finished with the manager you can use the internet browser or the PSN to play online with friends.
To have access to skins, you need to have purchased the full version of Minecraft. - Log into the Minecraft website - Go to your profile - Download the template skin - Open the template skin in an image editing program (paint, photoshop) - Edit the skin as you like - Re-upload it on your profile
IDM-Internet Download Manager is the fastest download manager. Several others like DAP, FDM are out there but idm comes with a large number of feature and has a very good internal accelerating process.
A server IP is an address that you use on the internet. You can also use it for minecraft. By the way, wat is zackscott's server ip? You don't have to answer it