Is there a bus from santiago international airport to the city of santiago?

I can't say with absolute authority, but I'm pretty positive there is no bus directly from the airport to Talca. You'd have to get a bus or colectivo into the center and then take the bus to Talca.

I believe that there is. However, if not, there is a frequent, inexpensive shuttle to the metro stop Pajaritos, where the bus station is. From there, there are a variety of buses to Valparaiso, Vina,...

It is the Capital and largest city in Chile

las Vegas, Nevada

Larnaca, Cyprus.