1) Diplomacy:
It seems impossible to win without focusing heavily on diplomacy. One has to anticipate when another player will DoW you (for example, a Atilla runs short of other neighbours and start to look at your land with a grim). Trying to have the other players fight each other (and especially making sure that the runoff civ is at war with a relevant opponent)
War is almost inevitably dictated by proximity. Look for your closest opponent and realize that he, in all likelihood, is going to DOW you pre-turn 100. Beyond that, yes, of course you'll befriend civs who aren't nearby. You'd do this regardless of the strategy that you're pursuing.
Because of that, I am not so much in favor of stealing workers. In ICS, you have to trade around 10-15 luxuries all the time against 240gold. If you have hostile or even war computeurs, you can't sell them and then you cannot buy your settlers.
Steal workers from City States, not computers >.<
I still manage to have only one opponent most of the time. Most of the games I lost where because someone declared war while my troopst where fighing elsewhere -> I think that trying to be friends is key
No, defeating your closest enemy is key. Always attack the computer that is closest to you. It's unlikely that another computer will randomly DOW you as long as you do. Unless you are playing on a small/tiny/duel map you should never be close to more than 1 at a time (especially early on). This is especially true given that computers have a natural tendency to expand towards other players. That is, the next closest player to you is, in all likelihood, going to expand towards someone else (and end up warring with him/her). I have almost never seen the computer expand "defensively" on deity. They will happily ignore big empty spaces in favor of aggressively encroaching on someone else's territory.
If 2 civs do DOW for whatever reason you are probably going to lose. Their unit spam is insane on Deity. While you may be ale to hold off early double-DOWs, mid-game ones should almost always crush you. Even if you do survive that's all that you'll be able to do. It's very taxing to wage wars on 2 fronts after all.
Although, the nice thing about Maya is their ability to grab an early GG for free. I've definitely picked one up early on and used it to slam a citadel near my closest opponent. When he DOW'd me he basically just ran his army in to it until he lost everything. Tricks like that are great for winning early wars with minimal losses/investments.
Also, something that I discovered a bit late is “si vis pacem, para bellum”: it is important to show a fat army to your neighbours just to avoid that they DoW you. Then you can choose your opponents. Therefore, continue to build / upgrade your army even if you do not plan to wage war short term.
You will rarely-if-ever outproduce the computers on Deity. A "fat" army should still be relatively small. If you do, it means that you should be looking to wage war in the short-term. There's no real reason to play passively while ICSing after all.
2) Science
I read in your guide to build a library before a monument. Also, often read that Messengers of the God is a must "epsecially with the Mayans". I completely disagree. With mayans, you already have the wonderful pyramid to give you +2science (and the faith to found early). What you need is therefore happiness to be able to continue spamming cities to get those +2 science or ways to have more settlers. Hence, I think that besides desert folklore which is OP, other situational pantheon are better:
- sacred waters (1 happiness near rivers) give you the needed happiness to continue spamming. It continue to scale in the game as if you wage war and puppet and have ca 20-30 cities late in the game, it is likely that you will have 4-8 happiness from that. Especially, if you have rivers, trade routes come late (as you need to have engineering which I think should come after Construction and theology -> late)
- culture stuff (from wine / incense or jungle or gold… is useful in your capital. The +4 / +6 culture you get will help you to quickly move on the liberty tree (especially to get the free settler or the +1 happiness from trade routes, both key to city spam). Also, it helps to expand borders on your capital, which is often useful to get luxuries within 3 hex
But obviously, if nothing situational make sense, MotG is very good. I just find that the trade routes arrive a bit late to get the benefit
For the same reasons, early libraries are useless: they will get you 1 science for your other cities, maybe 2, which early is nothing compared to spamming a new city which will build a pyramid
Libraries are needed for the NC. Civ is still a game of science and you'll need more than 2 science per city to maintain a decent tech rate.
Monuments are fine and you'll probably build them but I mean what is it that you hope to accomplish with the culture? How many policies are you unlocking in a 20+ city game when each city is only producing 2 culture? You are finishing tradition and that's basically it. Oh, sure, you'll start on another one, but that's about it.
My opinion is that science is the lifeblood of this game and that you can't effectively abuse culture while ICSing. As such, I typically value beakers over culture.
Sacred Waters is situational but ultimately it isn't very strong. It's usually at best 3 happiness early on which is when you need it the most. Some maps are obviously more generous than others but I mean on average that's what I expect to get from it in the early game. I would much rather focus on creating new cities and selling resources to buy up city states and such than worry about 3 happiness. MoTG may take a bit of time to kick in but it's the best way to maintain a good BpT count. You still have to hit key military techs if you want to win after all. It's not like you're going to win without things like bombers. I see far too many ICS strategies that don't care enough about science.
I build granaries, workshops... And always find an excuse thing to build instead of a good old crossbowman. I should probably just pump out more units to gain wars. Also, I hate loosing units, so I probably do not take enough risk. Maybe if I move my units earlier next to an enemy city, I will loose 2 but will conquer the city earlier and get a nice peace treaty…
Granaries are fine. You'll often want a chunk of your cities to hit 5 pop eventually (for Universitiy specialist slots). Stuff like Workshops are useless however since each city is building 4-5 buildings tops.