How would have "Endgame" played out if the other half was snapped away?

That's a fun scenario.

Let's look at Titan. If the others were snapped, that means Tony & Nebula would have disappeared, leaving Star Lord, Drax, Mantis, Dr. Strange and Spider-Man.
No doubt, the Guardians would have given Strange and Parker a ride back to Earth, so let's assume they stick around for now.

In Wakanda, we're left with Black Panther, Wanda, Falcon, Groot & Bucky. Shuri would also remain.
Nick Fury would still be around so it's safe to say he'd organize the leftover Avengers from Wakanda back at some kind of HQ.

And since Ant-Man would have been snapped instead of Wasp, Hank and Janet (who are all way more qualified in the intricacies of the Quantum Realm), I assume they'd be the ones to go the the Avengers with the 'time heist' idea.
Shuri is supposed to be even smarter than Stark, so I think she could figure out time travel, working with Hank Pym who knows all about the Quantum Realm.

Then it comes to actually taking the stones from the past.

Dr. Strange would immediately convince the Ancient One to hand over the Time Stone, since she knows him through time-stone shenanigans (even before they've actually met).
And with his powers he could easily open a portal to steal the Space Stone (Tesseract) and the Mind Stone (Loki's scepter) from the (newly formed) Avengers in 2012.

Star Lord actually retrieved the Power Stone the first time around, so he'd just go there a day early. Instead of getting the Reality Stone from Asgard, the other Guardians could take it from the Collector at Knowhere sometime BEFORE Thanos shows up.

Then it's the Soul Stone. With Gamora dead and Nebula snapped, how would anyone else know where it even is?
Maybe... and this is a stretch... but, maybe the Guardians could track down Gamora's body, leading them to Vormir.
Then they know to go back in time to get the stone. But who sacrifices themself like Black Widow?
My guess is Drax. He dies, allowing Mantis (who loves him, even if it's plutonic) to gain the stone.

Well the Pym particles were the crucial key.

Are you saying Ant Man would not be in it he was decimated and Hank Pym, his wife and daughter were left?

They'd still have the Pym particles then. Hank was a scientist who understood that field....off the top of my head that is there only shot because the time travel angle was the only option they left themselves. They'd need the stones without time travel and if Thanos still destroys the stones that takes away all other options.

Dr. Strange was still around....but without the time stone....what good is he? Of course.....if Tony is decimated, he wouldn't give him the time stone in order to save Tony.....the one in 14 million chance of winning.

It seems like Tony is the only one who could have figured out how control and navigate the time travel. Is Hank capable of that?

Eh, their best chance was to gang up on Thanos. If Wanda and Tony and Thor and everyone could have ganged up.....joined forces instead of always being split up.....fighting him in little groups here and there, that was their only chance.

Also, we were they caught off guard so? Why did Thanos know exactly where Vision was? How did they know where Dr. Strange was and that these people had the stones? If the stones were so easy to find why had it been such a quest to find them all these years?

Anyway if Vision and Strange had been able to join forces with their infinity stones and all the other heroes joined up in unison they could have won. I mean Vision was taken out of the fight before they even knew Earth was being attacked.
Also, if Dr. Strange can cut off that beasts hand with the portal circle.....if he can make Loki fall in that no where realm while he was talking to Thor.....it seems he could have cut up Thanos in those portals or banished if off to that realm and left him.

So many questions....so many possibilities. This story had so much going on.....they could have gone anywhere with it.

Well, since Tony needed to live for them to win it would have played out as a loss.

It also means, when Thanos snapped his fingers he must have consciously made an effort to ensure Tony was not among the soon-to-be disintegrated.