Servus librum in bibliotheca invenit et dominam vocat.

The subject is servus because it’s in the nominative singular (the “default” dictionary form for many 2nd-declension masculine nouns ending in -us). So servus is the one who both invenit and vocat.

Librum is accusative singular, used here as the direct object of invenit (what he finds). The noun is liber, libri (2nd declension), and its accusative singular ending is -um.

Here it means in the library because in is followed by the ablative: bibliothecā (1st declension ablative singular, ending -ā).
Rule of thumb:

• in + ablative = location (in/on)
• in + accusative = motion toward (into/onto)

It’s actually bibliothecā with a long -ā in the ablative singular (often written the same as -a in plain text). For 1st-declension nouns:

• nominative singular: bibliotheca (subject form)
• ablative singular: bibliothecā (used after in for location)

Both are present tense:

• invenit = he/she/it finds
• vocat = he/she/it calls
  In Latin, the simple present often covers both habitual (finds/calls) and “right now” (is finding/is calling) depending on context.

Because dominām is accusative singular (1st declension ending -am), which typically marks the direct object. So vocat dominam = he calls the mistress.

Only to invenit in the most straightforward reading:

• librum ... invenit = he finds a book
• dominām vocat = he calls the mistress
  Each verb has its own object: invenit → librum, vocat → dominam.

Domina is the feminine noun meaning mistress/lady of the house, so its accusative is dominām. If the sentence meant master (male), it would use dominum (accusative of dominus).

Latin word order is flexible because the endings show grammatical roles. You could see variations like:

• Servus in bibliotheca librum invenit et dominam vocat.
• Librum servus in bibliotheca invenit... They’d still mean essentially the same thing, though word order can add emphasis.

Yes. Et means and, linking two verbs with the same subject:

• invenit et vocat = he finds and (he) calls
  Latin often omits repeating the subject when it stays the same.