Can't reinstall OS X on old early 2011 MacBook Pro After Reset

So I was going to trade in my old 2011 MacBook Pro for a 2019 MacBook Air for my gf.

Okay just like the usual I was doing some 'factory reset' to delete all the data inside of it.

And just going to the last step before I can apply for the trade in, which is just reinstall the OS X, so the staff can check the condition of my MacBook Pro.

But I can't believe it can be such pain the ***. I already read almost everything but got no clue, I spend too many hours already just wanting to installing an OS.

First, this was the error:

Tried so many ways to solve it, including make couple of bootable USB from some sources, which is useless, it won't work anymore, idk why.

Then turn out simply use my sister's apple ID solve this problem, like what? that took a day to solve it. Very nice.

And after that, it was downloading the OS X, we are so happy to wait for it to finish.

But another error pop up:

Well, cool.

Ask the staff? My laptop was too old, try OS X Lion, alright:

Yes, including my sister's apple ID.

Now someone please help me, what I need to do next ?

I read online, suggest I should make a bootable USB from downloaded OS X from the apple store but from same aged device or lower.

Why they make it hard?

My MacBook still working good before the reset.

Now I don't know if I still want to buy my gf another MacBook or just simply get a windows laptop.

I never encountered this kind of problem entire life. Usually I can solve it easily.

I won't recommend apple product anymore, can't believe it, I was such a huge fan back then.

PS: My country don't have the Apple Store, only Authorized Reseller.