Learn Farsi: لیوان پر است.

In Farsi, impersonal constructions with enclitics (like سردم است, literally "my cold is") are used for living things experiencing a physical or mental state. Because the glass is an inanimate object and doesn't "feel" full, we just use the standard subject + adjective + "to be" format: لیوان پر است.

Does لیوان refer to the material "glass" as well as a drinking glass?

No, لیوان strictly means a drinking vessel (a glass or mug). If you want to talk about the material itself, like a glass window or a glass bottle, you use the word شیشه (shisheh).

How do I know how to pronounce پر if it can mean both "full" and "feather"?

Because Farsi doesn't typically write short vowels, you have to rely on context. Here, it is pronounced "por" (full). If you pronounced it "par", it would mean "feather"—and "The glass is feather" wouldn't make much sense!

How is this sentence pronounced in casual, spoken Farsi?

In conversational Farsi, the verb است (ast) is often shortened to an "-e" sound attached to the end of the previous word. Since پر ends in a consonant sound, you will usually hear people say لیوان پره (livan pore).