XBOX ONE S ALL DIGITAL WON'T STAY ON (QUARANTINE)

I am from India. I bought an Xbox one S all digital. From the start it had hiccups in performance, sometimes games would unexpectedly crash as well. I could notice the performance difference because I also have an Xbox one S. Everything was going smooth
until June 2020(8th month after buying). I was playing NFS Heat and I could see visual artefacts in my game. But I didn't care much because it was happening only in NFS HEAT. Every other game was working perfectly alright. But after a week COD Warfare started
having the same visual artefacts. That's when I knew the problem is not with games but with the system. Yet I wanted to make sure. So I downloaded Battlefield 5 for testing. Everything went well in Battlefield 5 and that night I slept. Next day I woke up and
my Xbox won't stay on. It turns on and nothing comes on screen. The fan and the xbox light runs for 1 minute 5 seconds and it turns off. I tried multiple times but the same issue continued.

I wasn't much worried because my console was still under warranty (more 4 months to go). But "fortunately" in India there's no official microsoft repair centers. And what available is local repair centers. I lost my hope but wasn't going to give up. So I
thought of checking what might be the cause. I checked online and again every xbox one consoles have a troubleshooting menu or called as a recovery mode which can be summoned by pressing power eject and bind key. "Fortunately" All digital don't have an Eject
key as it doesn't have a CD Drive. Then I was left with the only option of opening up my xbox to see what could be the possible issue. I opened it up to clean dust and found that my hard drive is making a beep/clicking noise in interval of that 1 minute 5
seconds for multiple times. Hence, I knew the problem was with the Hard drive and that's the reason my xbox isn't staying on.

Here are my questions.

1) Do Xbox one S All digital has a recovery mode like all other Xbox one's?(If yes, then how to access it?)

2) Is there a possibility that my xbox won't stay on because it is not able to read data from the Hard disk because it is faulty and so it initiates an auto shutdown after 1 minute 5 seconds?(Just to make sure that the issue isn't with my power supply unit)

3) I know I can replace my Hard drive by buying another SATA hard drive with same specifications but if I use the same procedure to format and make it ready for installation including external USB stick, do I need recovery mode to start up my xbox or my
xbox will detect my new hard disk and initiate all installations and can the issue be fixed?

Please help me. It is quarantine time and I'm going nuts without getting to play my games with my friends.

:)