Less then half? Half? Or more?

Far less than half. GOG has over 1300 games.

On any given sale, maybe a whole 1-5% goes on sale.

Usually about 10-20 games. And GOG has over 2000.

Do they usually do a good job rotating the games?

If you are interested in a few games and want to gauge the chances of them getting discounted in the near future, why not looking at price history with a tracker tool like isthereanydeal.com or similar.

Sadly, only part of the library is on regular "rotating". Plenty of games didn't had any discount since months, some even since years.

There are games which are constantly getting back to discounts. In fact if you would check sales from last 5-6 months, you could see (more or less) all games which are regularly discounted.

What, every week? No, that sort of proportion is reserved for the big 'seasonal' sales. It's a very small proportion for the normal weekly sales, maybe around 1%.

As Trilarion suggested, head over to Isthereanydeal.com, mark down the discount (50%, 70% etc..) that you want for the GOG game you are looking to buy (make sure you are using the correct game title that contains GOG prices), and wait for them to email you when the discount happens.

Usually about 100 titles or so but that counts DLC and deluxe editions out of the catalog which is currently 2356

Do you have info on how many games have NEVER been discounted on GOG before?

Titles released more than 1 year ago, it's only DLCs:
Ashes of the Singularity: Escalation - Epic Map Pack DLC
Ashes of the Singularity: Escalation - Inception DLC
Ashes of the Singularity: Escalation - Oblivion DLC
Factorio Soundtrack
Galactic Civilizations III – Mech Parts Kit DLC
Galactic Civilizations III – Mercenaries Expansion Pack DLC
This War of Mine: Stories - Season Pass

Honorable mention - released 18-Jan-2018:
Offworld Trading Company - Limited Supply DLC

This does exclude games which never were on sale but experienced a price rise which was the case for Factorio, I believe. Not sure if there were others.

There are 51 titles released in the last year that have yet to go on sale. 52 if you count Cultist Simulator: The Dancer DLC which was only on sale for 6 hours.

Base games without a sale - 14:
Battle Princess Madelyn (6-Dec-2018)
Empires of the Undergrowth (9-Mar-2018)
Fight'N Rage (10-Jan-2019)
Gekido Kintaro’s Revenge (9-Jan-2019)
GRIS (13-Dec-2018)
Kingdom Rush Origins (19-Oct-2018)
Kynseed (8-Nov-2018)
Mana Spark (11-Jan-2019)
Mutant Football League: Dynasty Edition (30-Oct-2018)
Orphan (31-Oct-2018)
Project Warlock (18-Oct-2018)
Return of the Obra Dinn (18-Oct-2018)
The Bard's Tale Trilogy (14-Aug-2018)
X4: Foundations (23-Nov-2018)

Thanks guys.