Android - How to use Android in Wi-Fi repeater mode by bridging Wi-Fi with Access Point?

That's not worth the trouble.

It's not supported out of the box by Android and you would have to (re)compile and configure and script many things. The dedicated router is the more reasonable and stable solution (and it's also cheap).

Reasons are the following. You would need:

• USB host support
• finding a USB wifi module that's supported by linux
• Compile a kernel module or a new kernel (to support the USB module)
• bridge utilities (maybe), bridge module in linux
• a working wpa_supplicant binary for the new USB dongle
• time
• 17EUR+ costs (Wifi USB dongle (starting around 12EUR) + USB OTG cable (5EUR))

In contrast to this the cheapest repeater-mode wifi router I found on Amazon was 18EUR and requires null additional fiddling (plus has a better antenna).

Using wi-fi and hotspot at the same time is not a standard feature introduced in stock Android or custom ROM's so far (AFAIK). There are apps that makes it possible using Wi-Fi Direct. However you can do this manually too if you are comfortable with commandline usage. Even a USB Wi-Fi dongle is not needed if managed and AP modes are supported simultaneously by wireless chip.

For details see my answer to How to use Wi-Fi and hotspot at the same time on Android?