Question about Huawei E5377: LTE/HSPA mobile modem

I used this part abroad for 3 weeks.
1) Yes, it has a repeater function. However, it will probably only work if you get the SSID, username and password. This was the case in all our hotels.
If the WLAN is realised via a so-called landing page (guest WLAN where you have to register via a website), I don't see any possibilities to use the device as a repeater. Or in other words. It always works if you can enter the password in the WLAN settings of your smartphone, but not if you have to go to a website afterwards to authenticate.
2) I don't have one, but I would have been happy to boost the Wi-Fi signal. It's important to note that these external antennas are designed to boost the 3G/4G signal, not the Wi-Fi signal. However, amplifying the Wi-Fi signal would be more practical on campsites. Nevertheless, the device has done a good job. If you only have reception at one end of the room/tent, you can place the receiver there and use the device to amplify the signal throughout the room. A small power bank can be useful if there is no power socket nearby.

In the end, I used the device 90% as a repeater in hotels and 10% in 3G mode on the road.

Note: Funnily enough, this device came in white, although I had previously been looking for a white one and had already given up.