Learn Arabic (Modern Standard): أنا في البيت.

There is no word for "am" here! In Arabic, you do not use the verb "to be" (am, is, are) in the present tense. You simply put the subject أنا (I) right next to the phrase في البيت (in the house) to make a complete sentence meaning "I am in the house."

Does the pronoun أنا change if a woman is speaking instead of a man?

No, أنا is completely gender-neutral. It means "I" for both men and women. This is different from the independent pronouns for "you" and "he/she", which do change depending on gender.

How do we know it means "the house" and not just "a house"?

The prefix الـ (al-) attached to the beginning of البيت is the definite article, which means "the". If you wanted to say "in a house" (indefinite), you would drop this prefix and just say في بيت.

Why do we hear the "L" sound clearly when pronouncing البيت?

The letter baa ب in البيت is what we call a "moon letter". This means the "L" sound of the "the" prefix (الـ) is pronounced clearly. If the word started with a "sun letter" instead, the "L" would be silent and the first letter of the word would be doubled or emphasized.