I wonder if the Caesar 3 download offered by GOG contains the patch that enables you to turn off the god effects? Can anybody please let me know?

I don't know.

But I highly recommend anyone wanting to play Caesar 3 just grab the open-source reimplementation of it: https://github.com/bvschaik/julius

This one aims to be vanilla compatible with just a little bit of UI polish and modern system compatibility, and that makes all the difference. It runs properly in a window and at any resolution, it runs smooth at high speeds, it can (optionally) display some info like unemployment rate in the side panel, if you don't want to click through advisors every time.. it can (optionally) display the range of fountains, wells, and reservoirs when you're building them. It fixes a few visual glitches, such as aqueducts leaving an intersection (until you rotate camera) after the intersecting part of it is deleted. You can set warehouses to "not accept" everything with one click instead of clicking each item separately. It does have a few toggles for turning on just a couple bugfixes that affect gameplay (you don't have to turn them on though).

And it does indeed have the option to turn off god effects.

Absolutely superior to vanilla in every way, with no forced gameplay changes that would make it into something different. Heck, it should even be compatible with vanilla saves.

For those who want additional gameplay changes (e.g. road blocks), there is a fork of Julius called Augustus: https://github.com/Keriew/augustus

Yes, it can be disabled in GoG version.

About open-source remakes - it's most likely trash. That's completely different game written using a different coding language which plays differently. Only vision of an old game. Why just not make a new game with own game logic and rules and not kick the dead horse?

Why do people see source ports as trash?

Especially when they're often the only way to run the on alternate operating systems. Don't see anyone making cartridges for Maniac Mansion, but there exists a version of SCUMMVM (and therefore) Maniac Mansion for N64.

Original games are played back and forth and have the same reproducible errors and patterns of user experience. So-called remakes are in a state of never ending change and user depends on a whim of "re-maker". For example OpenXCOM seems to be slightly different in how AI responds to the threats. Jagged Alliance 2 re-make Stratiaccella known for dissapearing Chalice, one-time unique artifact which can be sold for big amount of money or citizen loyalty. I would not be surprised if remakes have more bugs than original. Perhaps the only reason to install them is to deploy on an unsupported system as you said. But let's make no mistake here: under the hood it's a different game with the same name and visual art.