Generally good to give in to AI demands. The exceptions would be if you literally don't care at all about them, the demand is for gold, or you think it's important to keep that specific tech away from them - an example of this would be not giving Monarchy to someone if you're gonna be attacking in a dozen turns, because that might help them get Feudalism for longbows, or not giving Aesthetics to someone while you are building The Parthenon. Cyrus is one of the higher-performing AIs in general, but he's also a pretty friendly neighbor if you manage him well. Get him to "Pleased" status and he's a good trustworthy friend. Nothing wrong with giving him Writing.
Tech trading in general is a good thing. Be aware that every AI has a hidden counter of how many times they've seen you get a tech in trade (from them or anyone else); when you go above a threshold on that counter, they start saying "We fear you are becoming too advanced" and refusing to trade more techs with you unless you are "Friendly" relations to them. So really garbage techs aren't always good things to get if you have no particular use for them; e.g., you'll probably want to simply skip Archery this game.
I strongly dislike the spot 1W of the lake for an 8th city. It has zero forests to chop and zero good tiles to work prior to a border pop. Which means first you'll need to (slowly) build a monument or granary. Then you'll need to (slowly) wait for 10 culture for a border pop, then build the gold mines. And you'll also be relying just on some ordinary riverside grass farm tiles to grow on, so simply getting up to size 4 (which you'd need to work both gold tiles and not starve to death) will take a while. Maybe 30 turns after you settle there you might be working the two gold mines, which is a really long time. You'd basically be sacrificing a 100-hammer settler to free up a 15-hammer Quechua.
1N of the lake is a small improvement. 1 tile closer to the capital, no border pop needed. Still slow to grow up to size-4, but probably a good 10 turns or so faster. That's like 150-200 more commerce.
My personal preference for getting those golds would be the plainshill 1W of the stone near Machu Picchu. It captures one gold right away, and the other is gonna be caught by Tiwanaku in about a dozen turns. Borrow the pigs from Cuzco long enough to grow to size-4. Take one floodplains tile from Machu Picchu, drop a farm on a grass riverside tile, build a pair of mines on the gold. There's a solid size-4 pocket city; floodplains cottage, grass farm, two gold mines. 6 hammers and around 20 commerce per turn pretty quickly.
The plainshill + fish city site is a nice one, and definitely rising near the top of the priority list. Chop a work boat, build a second work boat to go exploring the coastline south (hopefully hook up some other countries to your trading network), pasture the horses, build + whip a library, run horses, fish, 2x scientist maybe. The extra horse would let you trade with Cyrus, start building better diplomatic relations and maybe get something useful in return. Far west pigs are a bit of a stretch right now; I don't think your empire is ready for the logistics of making that city site productive yet. Maybe when you've got a few more military units and another half-dozen workers.
It's generally not good to whip wonders, because you get reduced rate of return. Whips normally give 30 hammers per population sacrificed, but with wonders it's only 20 per pop. However, there is a little micro trick that's good to take advantage of. Overflow hammers from whips can move into wonder production without penalty. For example, you could start an axeman in Cuzco 2 turns before you're ready to start Pyramids. Adjust the tiles Cuzco is working so, on that turn, it produces exactly 4 hammers. That way one turn before you start the wonder, your axeman is at 4/35 progress, with 31 hammers remaining. Because you get 30 hammers per pop, 31 hammers remaining requires a 2-pop whip. 29 of those hammers will be overflow and move onto starting your wonder next turn (plus however many hammers the city itself produces that turn). Pair that with the fact that you're an Industrious leader, have stone, and could chop a couple forests that turn as well, you might easily hit 200+ hammers on the very first turn of your starting Pyramids.
Theoretically, you'd hope to have a couple mines on hills near Cuzco, and there's nothing wrong with it growing up to size 5, 6, or 7 while making the wonder. But you're short on workers and it's not a huge priority; more important is improving the tiles your other cities need to be working, and chopping forests (chops will contribute to the wonder faster than mines will pay off).
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