Can iPhone 6 with iOS 12.5.5 be upgraded to iOS 13

The iPhone 6 is not compatible with iOS 13 or higher. It can be not updated further.

Encorecircle ~ No, iPhone 6 cannot be updated beyond iOS 12:

iOS 13 and iPadOS are compatible with these devices

...Found by searching Apple's Knowledge Base.

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How about to download apps that needs ios 13?

Purchase and use an iPhone that can support iOS 13 or later.

That includes all iPhones released by Apple within the past seven years.