Gracias; te llamaré más tarde.

Yes, it can be. A semicolon (;) in Spanish works much like in English: it links two related clauses more strongly than a comma but less strongly than a full stop.
That said, in everyday writing you’ll more often see:

• Gracias. Te llamaré más tarde. (most common)
• Gracias, te llamaré más tarde. (also common)

Spanish often drops subject pronouns because the verb ending already shows who the subject is.
Llamaré clearly means I will call, so yo is optional. You’d add yo mainly for emphasis or contrast (e.g., Yo te llamaré, no él).

Llamaré is the simple future (futuro simple): I will call.
Formation: infinitive llamar + future ending -é (for yo):

• llamar + é → llamaré Other forms: llamarás, llamará, llamaremos, llamaréis, llamarán.

The accent in llamaré marks the stress on the last syllable: lla-ma-RÉ.
It also helps distinguish future forms and keeps pronunciation consistent with Spanish stress rules.

Te means you (informal singular). In te llamaré, te is the direct object pronoun: I will call you.
With llamar (por teléfono), Spanish commonly uses a direct object: llamar a alguien → llamarte.

With a noun, you use the personal a: llamar a Juan.
With an object pronoun (me/te/lo/la/le/nos/os/los/las/les), the a is not used: te llamaré, not a te llamaré.

Yes, te is for tú (informal singular). For formal usted, you’d use:

• Gracias; le llamaré más tarde.
  In Spain, for informal plural vosotros, you’d say:
• Gracias; os llamaré más tarde.
  For formal plural ustedes:
• Gracias; les llamaré más tarde.

In this context, te llamaré más tarde is most naturally understood as I’ll call you (on the phone) later.
Spanish llamar can also mean to call/name (e.g., Me llamo Ana), but the structure te llamaré más tarde strongly points to a phone call.

Más tarde means later / later on. It’s flexible: it could mean later today or later in the future, depending on context.
Common alternatives in Spain:

• luego = later / then (Te llamo luego is very common)
• más tarde can feel a bit more “not right away” than luego, but they often overlap.

Yes. Both are correct. In Spain, Te llamo luego (present used for near future) is extremely natural in casual speech, while Te llamaré luego is also fine and a bit more “future-marked.”

Yes. A very common spoken option is:

• Gracias; te llamo más tarde.
  This present tense often implies a planned near-future action, similar to English I’ll call you later even though English uses will.

With ir a + infinitive, the pronoun can go before the conjugated verb or attached to the infinitive:

• Te voy a llamar más tarde.
• Voy a llamarte más tarde.
  Both are correct; the choice is mostly stylistic.