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For your first question, by rooting the phone, you can remove a lot of the "bloatware" the manufacturers and phone companies add. You can download apps that need root permissions, such as certain 1 step cache cleaners.
By rooting and installing custom ROMs, you can change the whole look and feel of the phone. I rooted when 2.1 came out, as on the Original Droid, it took away the ability to have led lights blink while screen was ON, which made using any dock useless,and I risked nit getting sms from kids if I was watching a video or tv on phone while at the gym. Rooting and installing Cyanogen ROM fixed this.
Not all ROMs do that though, such as MIUI. Many ROMs also include the battery features you want, but there are apps in market that do this as well.
As for installing apps from market, I am confused on this question. Open market. If app is available for your phone, download it. If it isn't free, some have trial periods, or free versions (with ads....) Or, purchase it...
Oh....rooting also allows you to download apps to get rid of the add you may see....
Hope some of this helps!
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