Hi MioNM11
welcome to the Apple (user-to-user) Community!
Re: "After i order to pick up in store, how many days do i have for collecting it?"
We are all Apple users, like yourself, in the community, and pickup options may depend on the store you choose.
Seems best to consult with a shopping specialist to arrange a suitable pick-up option when you are placing your iPhone order. Eg: There's a link for that on: Buy iPhone - Apple
or
You may want to contact a particular Apple Store for their pick-up options: Apple Store - Find a Store - Apple
More info:
You can scroll down to "Apple Pickup" in Apple support's online article:
Shipping & Pickup - Shopping Help - Apple for the way Apple does pickups.
Eg: says:
"Pickup Notification: Once your items are available at the Apple Store, we'll send a pickup notification email.
Pickup Reminder: We'll send a reminder email if your item is still waiting to be picked up."
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Re: " i will be in the US in 13 days"
Wondering if you are aware there may be warranty (or repairs under warranty) restrictions from Apple in other countries, for US purchases. Eg: Apple's document: Legal - iOS Warranty Document Us - Apple says:
"IMPORTANT RESTRICTION FOR iPHONE, iPAD, APPLE TV, HOMEPOD, AND APPLE VISION PRO SERVICE.
Apple may restrict warranty service for iPhone, iPad, Apple TV, HomePod, and Apple Vision Pro
to the country where Apple or its Authorized Distributors originally sold the device."
All the best :-)