Learn French: Le président a parlé en tant que mentor.

This is the core rule for en tant que. When expressing a person's role, profession, or status, you drop the article. The noun acts almost like an adjective describing the capacity in which the person is acting.

Could I just say comme mentor instead of en tant que mentor?

Yes, comme mentor is also correct and means essentially the same thing. However, en tant que emphasizes the official capacity or specific role a bit more strongly. Note that if you added an article and said comme un mentor, it changes the meaning to a comparison: he spoke like a mentor, implying he might not actually be one.

Is there a liaison between tant and que in this phrase?

No, the t at the end of tant remains silent. However, there is a mandatory liaison between en and tant, so the first part is pronounced as en-(n)tant.

Why is a parlé (passé composé) used here rather than parlait (imparfait)?

The passé composé (a parlé) treats the speaking as a completed, distinct event, like a single speech or a specific conversation. If you used the imparfait (parlait), it would set a background scene (he was speaking) or describe a habit (he used to speak).