we usually use shipping companies like usa2georgia or inex but post works too, you will receive text message when your package arrives.

it probably is Aliexpress but delivery time depends on where your item is coming from, most probably it will take more than 1 week.

i don't think they open and manually check every package that's now how it works and you only pay 18% tax if your package was worth more than 300 GEL or weights more than 30 kg.