Αυτός ο κανόνας ισχύει μόνο στο πανεπιστήμιο, όχι στο γραφείο.

Yes. Αυτός is a demonstrative (roughly this) and it agrees with the noun it modifies in gender, number, and case.

• κανόνας (rule) is masculine, singular, nominative here (it’s the subject).
  So the demonstrative takes the masculine nominative singular form: αυτός.

ο is the definite article (the) in masculine nominative singular. Greek commonly uses the article even when English might not, and demonstratives typically appear with the article:

• Αυτός ο κανόνας = This rule (literally This the rule)

Many masculine nouns in Greek end in -ας in the nominative singular (one common masculine pattern). Here it’s just the dictionary form of the noun:

• ο κανόνας = the rule
  (Other masculine nouns might end in -ος or -ης, depending on the pattern.)

ισχύει means is valid / applies / is in force.
It’s 3rd person singular present tense, because the subject Αυτός ο κανόνας is singular:

• (This rule) ισχύει = (This rule) applies

No. Greek verbs already show the person/number, and subject pronouns are usually omitted unless you want emphasis or contrast.
In this sentence, Αυτός is not a subject pronoun; it’s a demonstrative modifying κανόνας (this rule), so it belongs there.

στο is a very common contraction:

• σε + το = στο (in/to the)
  So μόνο στο πανεπιστήμιο literally means only in/at the university (context decides in/at).

σε/στο can cover both location (in/at) and movement/direction (to). Here the verb ισχύει (applies/is valid) describes where the rule is valid, so it’s understood as location:

• applies only at/in the university
  If the verb implied motion (like πάω = I go), στο would more naturally mean to.

Both πανεπιστήμιο (university) and γραφείο (office) are neuter nouns, often ending in -ο in the singular. Neuter nouns take the neuter article το, which becomes στο after contraction:

• το πανεπιστήμιο → στο πανεπιστήμιο
• το γραφείο → στο γραφείο

They’re related but not the same.

• δεν is used to negate a verb: δεν ισχύει = it doesn’t apply.
• όχι is used for contrast/“not … but …” or as no/not in answers.

Here you get a contrast structure: only X, not Y

• μόνο στο πανεπιστήμιο, όχι στο γραφείο = only at the university, not at the office

The comma marks a contrast/add-on phrase. It separates the main statement (applies only at the university) from the contrasting clarification (not at the office). In Greek, this kind of short contrasting phrase is often set off by a comma for readability.

Yes, Greek word order is fairly flexible because endings show grammatical roles.

• Αυτός ο κανόνας ισχύει μόνο στο πανεπιστήμιο… is neutral and straightforward.
• Μόνο στο πανεπιστήμιο ισχύει αυτός ο κανόνας… front-loads emphasis on only at the university.
  Both are correct; the difference is mainly focus/emphasis.