Question about Garmin fenix 7X Solar

"esim lte" is incomprehensible.
It probably means eSIM LTE.
Answer: the Fenix 7X has Bluetooth and WLAN and is paired with WLAN and a smartphone, which naturally has a SIM card and 5G (LTE). To fully utilise the Fenix 7X, smartphone+Internet+BT+WLAN are required.
Without network coverage, the watch records all data offline and makes upload available as soon as the network is available.

No

No, she did not