Beer Talks!

1.
"The girl chugged a glass of beer down and stepped off the stage."
Does "chugged a glass of beer down" mean that she drank it?

2.
"On the bar in front of him rested a half-empty pitcher of beer that he guarded jealously,...he nursed his beer slowly but continually..."
Guarded his beer jealously? What was he doing? Does "nurse" here mean "drink"?

3.
"He took another guzzle of beer, sudsed it in his mouth."
What does "suds" mean as a verb here?

Chugged means drank very quickly.

Guarded jealously means that he let no one else near it, and certainly did not share.

To nurse a drink is to sip it slowly, making it last for a lot longer than usual.

To suds something is to literally make it form suds; to swish it around until it bubbles up.