So my thoughts on the proposed ideas for changes are below.
(although I wish you would make some basic overall changes first, before changing things that impact strategy - examples: why do the forum, the ingame forum, and the ingame clock all use a different time/date format? Why do you have multiple names for the same unit (demo ship vs fireship)? Why do explanations of some units and buildings make them sound like they are better than they are (tower: "...turns your polis into a nearly invincible stronghold against attackers." - so not true. myth unit erinys: "they are the most feared opponents to anyone alive" - when in fact they suck)
Horsemen: I don't think the problem with horsemen is that they are too weak (although boosting them up some is an idea I like). I feel the problem is the combination of recruit time and resource cost. Slingers are faster and cheaper, and when you want to push out maximum offense, slingers win. I don't think the extra 5 pts of offense will actually make a difference. I think you would need to change a lot of things to make a significant difference in what units were built. Perhaps the most significant but simplest change would be increasing the distance in defense values vs offense values across the board although I think a better tactic would be a combination of the following:
-- If offense loses, don't have all attacking units die in combat, and the stronger the unit, the more survivors (or allow for a retreat percent when in combat, and allow units to stop engaging when percent is met, and weaker units lose more when fleeing)
-- Allow for more building specialization. Barracks at lvl XX allow stables. Stables increase horsemen stats as they go up in levels.
-- Allow for a center special building that boosts only one type of unit offense / defense (thus making your primary unit more powerful - but only that unit)
Catapults: It is my understanding that catapults are rarely used because:
1) You want to conquer the city you are attacking, and if you destroy the wall to any degree, keeping the city would require an exponentially higher amount of defensive troops. Smash the wall to 0 and try to defend it vs ground assault (or myth assault - have never figured out if you classify flying units as ground). It's not worth the effort.
OR
2) If the defender has a significant force in place (say 10k population of troops - with a significant amount being swords) then you can hit the city with 20 or 30 cats / max slingers and still simply lose all attacking units with NO wall reduction at all. I don't quite understand how losses are determined (I understand how to determine winner vs loser, but have never seen how the number of units lost is figured), but when 30 cats can be lost with no benefit at all, it makes it hard to want to build them.
Possible ways to make cats actually useful (in addition to not all of them being destroyed as per above suggestion)
-- make catapults (or any ranged attacker - although you'd have to change what ranged does then) actually fire first, and damage the wall before close combat and wall bonuses to close combat occur
-- allow catapults to damage more than the wall in all worlds, not just hero worlds with extra research
-- add a new ship type that has catapults built on it, so one or both of the above ideas can be implemented; and that if breakthrough has been researched can actually damage a wall without land units being put into play even if defensive ships are in the harbor
Triremes: When doing the math, a combination of a single light ship and a single bireme is always better than the trireme when comparing population used. Why have a "super" unit that still falls short of the basic units. And to upgrade the trireme so it's still slower than the basic unit makes me question how you determine the value of units. Power wins. Speed wins. The two together are what everyone (that knows how to play the wargame aspect of grepolis) focuses on. If you make a "super" unit that fails to be superior to the basic units you still have a unit no one will play with (unless they don't understand why triremes suck to begin with). Why in the world would you want to research something that isn't better? It is my sincere belief that if you want the trireme to be considered, you have to
1) make it significantly better in multiple ways but
2) give it a debilitating factor that makes players consider using it anyway, but not in all cases
If you can't find that combination, players will either always use it, or never use it, which is what you have now.
Demo ship / fireship: It is my belief that the fireship is useless because of the combination of the following:
1) It cannot be used to attack (speaking of: why is it that the only way a person learns this is if they try to put it in a non-CS attack, and get an error message? Shouldn't all units have full disclosure on what they are and what they do??)
2) They attack last, making them useless in almost all cases
3) They cannot target a CS or transports.
4) They are insanely slow.
These are the negatives to why fireships don't get researched. So by the time a player might be in a position where they are being hit over and over with LS attacks to make them say "yeah, mathematically I'll win the BP war if I build a fireship" they either can't stop the attacks anyway, or they can simply ask alliance mates "can you stack my harbor with biremes please". All in all, taking time to research them won't change if the four negatives above don't change. But if they do decide to research/build them, they still get taken out by LS (or a smart player sends birs to attack and take them out) or they aren't building biremes and the attacker then sends ground or CS attacks and the fireships are useless anyway.
Researches:
You say: "The plow is the most favored research in the game, closely pursued by ceramic. Both researches are done in nearly all cities. On the other hand, diplomacy, espionage, cryptography, meteorology and breakthrough get researched seldom"
That's because what matters in the game is population space and rebuilding as much and as fast as possible, thus maximum resource space. If you can't compete with what will actually make you more threatening, you wont get researched. It's really basic, and I find this entire set of potential changes to be disappointing because all you are doing is either failing to understand that, or making a few changes in the new "best set of items to research". I don't see the win-win here of making all researches equally needed.
The same is true with your special building changes. Unless the buildings equally allow you to have an advantage at winning, all you will do is change the set of buildings that get built. Who won't build a war council in an attacking city? No one...
Overall:
I like some of the ideas and theories, but unless you actually make a more significant change or change strategy in a grander scale, you will fail to get the results you desire, and simply get new sets of "whats best".