They use riddell. Check out the website www.riddell.com
Yes, I play football at the Pro level and there are many skilled position players as well as special teams players that only wear shoulder pads and helmets.. In practice we sometimes only wear shoulder pads and helmets we call it pro-pads we also wear this during training camp a lot and when we are not going to hit full speed.
Most NFL players wear a jockstrap, and some wear a cup
High school and college players are required to wear; helmet, mouth piece, shoulder pads, hip pads, a butt pad, thigh pads, knee pads, and clears. A lot of the time you'll see nfl players not using their knee pads and or thigh pads bc they aren't required
Majority of NFL players wear oakley visors.
You can. NFL players can wear any glove they want but they have to have an NfL shield on it.
They are actually known as 'Sideline Jackets' and are a form of a parka. They are specially designed to accomodate the pads of the players. For more information, please refer to the related link.
A lot of players don't wear pads in their pants, because they believe it will slow them down; whether it be speed, agility, or simply, reaction time. This is why so many players object to the NFL's new rule in the 2013 season, stating that it will become mandatory for players to wear thigh and knee pads. Personally, I agree with the players. In college, I wore Yeh smallest(youth) pads I could find, and during my stint in arena and semi-pro, I NEVER wore them... So it kind of makes sense to me.
No, they don't have to wear mouthpiece.