Hello, I use the Netgear EX7300 Night Eagle X4 to amplify the signal on the floor, and I am very satisfied,

Certainly. You log into the WLAN with the repeater as you would with a computer. The repeater takes over the settings of the router. Make sure that One WLAN Name is activated, otherwise a separate network will be created with YOUR_WLANNAMEN_EXT. It is advisable to carry out the first configuration via a smartphone, as problems can occur on the computer and you may not be able to configure the repeater at all. Once configured, however, it is no longer a problem.

Try to connect a PC/laptop to the unit. Then go to the link in the operating instructions. After that, it should work perfectly. For me, it was pretty quick and uncomplicated.

Same SSID

For gaming I don't know...! For Live Streaming I think so...I watch TV with Netflix at UPC and I never had problems with "perfect picture and sound". I had to make an Access Point connection because the wifi link for the Extender mode was too far. I had to make an Ethernet cat 5e connection from the UPC modem and the 70m long Netgear device, the wifi connection with the mobile phones was perfect.

I do not know whether the mesh function can also be used in access point mode. I use the EX7300 as a wifi repeater. I can use the same SSID for the outgoing network. Switching between these networks works perfectly and the network is amplified very well, the WLAN signal can be received in almost the entire neighbourhood :)

I don't know the Internet Box 2. But I would measure the speeds directly on this box and check whether 1Gb is really coming or not. Do this via Ethernet and also via WiFi. Because the EX7300 cannot forward more than it receives. Then the location of the EX7300 is also decisive. The range in the 5GHz network is much smaller than with previous solutions because of the high frequency. From experience, it also needs line-of-sight in both directions. Anything else can affect the throughput. In case there is no line of sight to the box, an Ethernet line directly to the Netgear can be useful. Netgear offers a WLAN analysis app for Android that might be helpful for measurements. I also tested my device for a long time. But I don't have 802.11ac. So even at lower speeds it's tricky. My device is now in line of sight with the base unit. So it works for me without loss.

In the upper frequency band (5.47 - 5.725 GHz), this will certainly support DFS, as it is mandatory in Switzerland. This will probably not be the case in the lower band, as this is intended exclusively for indoor use. Since the DFS check can take up to 10 minutes, depending on the frequency, it would also not be particularly user-friendly.