Notification saying "Time is running out, Renew now" for Xbox GamePass Ultimate when months...

It's an ad. Like any subscription service, they'll try to get you to renew. Just ignore it if you're not interested. That tile usually changes from time to time, showing different messages or offers.

So my regular subscription will just continue after the 6 months is up?

No. If you already had xbox live gold then when you add an xbox gamepass ultimate subscription (which includes Xbox live gold) it upgrades your existing Xbox live gold subscription to gamepass ultimate (hence why your gold subscription "disappeared")

So lets say for example before you added the gamepass ultimate subscription you had 6 months of xbox live gold left. When you added the 6 month gamepass code youd essentially now have 12 months of gamepass ultimate in this above example.

Did you mean xbox gamepass ultimate and upgraded time or the free 6months they were giving out in india ?

They don't have 6months otherwise as it's a 1 month or 3 month membership

If it is xbox gamepass ultimate pc with upgraded time then no you forfeit it

No, They are not. I had GamePass PC earlier and everything used to work properly but then one day I got notification that there is an offer on GamePass Ultimate so I upgraded but since the day GamePass PC subscription ended and GamePass Ultimate subscription started, I can only launch games that are on EA Play and that too from EA Desktop App only.

Now, because the GamePass Ultimate was a 3 month subscription, so I can't even go back to GamePass PC until it's over.

Any game that launches from Xbox app for Windows fails to launch and tried repairing and resetting the Xbox and Microsoft Apps, sign-out and then again sign-in on both the apps but still same thing.

For Example, Forza Horizon 4 used to work earlier but now it does not.

By "xbox live" do you mean xbox gold? If you are adding gamepass separately to gold then you might as well just upgrade to the gamepass ultimate. All the current months will convert to gamepass ultimate. Buying them separately will only be a hassle rather than buying them in one package in ultimate. That's also the only way to keep the auto renew date the same is if you upgrade to the ultimate gamepass.