Here are all answers on your problems

Diplomacy is a problem, especially the diplomacy skill stat. Players are not bound to make friends or enemies based on a diplomacy stat, and an attempt to do so would be highly limiting of strategy and diplomacy. As an alternative, prehaps a population could approve or disapprove of policies, and a player would incur certain penalties(perhaps morale penalties, perhaps political penalties) for acting against their population's wishes (especially in cases as declaring war or accepting or rejecting trade proposals). While a player could exploit this by making seemingly reasonable proposals that a player, for reasons evident to a human player, must reject, so as to cause that player to incur the political penalty. However, this would require the political ability to communicate with someone frequently (if diplomatic skill rating does no currently affect this as the super diplomat ability does then it could be changed to do so for the purposes of multiplayer) and would lose the valuable ability to communicate to a given player at a moment's notice. This solution is far from ideal, but way work.
The diplomacy is in fact the key-problem. The points system will be the best:
If you disagree for proposal (and for AI this is great proposal fe. selling technology, planets, make peace treaty) look to your diplomacy ability. If your partner have grater than you, then:
a) your morale grow down - more, if the partner's diplomacy ability is higher

your senate can disagree with you, and agree with the partner requests (even if your party controls senate)
Many other areas of gameplay would perhaps need to be changed or tweaked, from combat to victory conditions to turn order. Please volunteer your suggestions and comment on/adapt other people's suggestions, or at least point out areas that would need change that have yet to be covered.
Original victory conditions:
-Influence: The best influence after X years (proposal)
-Ascending (ok)
-Technology victory (ok)
-Conquest victory (ok)
-Alliance - ok, but winner player with best influence
Proposals:
-Owns X percent influence in galaxy
-Has the highest score/rating after X years
-Exceeds second place total score/rating by X percent
-Ethical victory (as alliance)
-Alliance victory - this is big problem, because many players build "secret" alliance with advanced tech trading and destroy other players one by one. I cannot how solve it...
The length of a game of galactic civilizations is prohibitive for a multiplayer session.
Why?
The game can be ended after X turns (X years) and the winner is with the best influence or the best score/rating.
It is better solution than "conquest victory".
If one were to have multiple sessions, then organizing and reuniting players would be difficult to, for ten player maps, almost impossible.
If that is turn game, use PBEM mode: all players give orders (sent file to host) and receive solution. It works for SE-IV PBEM game.
All moving orders will be generate automatically (the player should see only the way), auto attack (when this same grid field or next), invade is special order (not only move)
The length of a turn is prohibitive, as a large amount of the time, up to nine tenths of the time, that one is playing is spent waiting for other players turns. This is even more of an issue when combined with very lengthy turns in the later game.
The PBEM system solves it. The new turn is ready when the host wants

Diplomacy is an issue when human players do not follow rules of diplomacy points or other traditional AI checks such as ethical alignment.
If the difference between diplomacy skills will be higher then:
a) the senate should have more chance to not allow this proposal (if player disagree)

the morale grow down
Ethical alignment: if alliance and different ethics

the morale grow down

the tourism grow down
Communication is an issue when players ideally can communicate for banter or game discussion or any such thing, yet would not become a source of alliances. On second thought, perhaps the communication system could be integrated with an altered version of the current diplomatic system into a new diplomatic system emphasizing deal-making and deal-breaking.
Communication is OK. Please add "see to all".
First turn: request
Second: the answer
The current diplomatic and cultural victory conditions would be unattainable , as the last player to take their turn before a player claims victory would be forced to delare war on the player who would claim victory. Victories could only result from conquest, ascension, or research.
The PBEM system solves all these issues: all playes have in this same turn this same information about "victory in X turns".
Human players would handle technology trading differently. While not necessarily a problem, it is possible that this could lead to gameplay imbalances in favor of diplomatic or research-oriented playstyles. It is certainly worthy or consideration.
And where is the problem? The human player will trade techs, or trade fazor-VII ships to other player per 1bc/ship
If the rating/score is calculated as sum of techs, influence, ships... that you helps your opponent.
Solutions:
a) use one tech tree for all races

use different tech tree for all, but race don't understand special techs for other race form other tech tree (cannot use improvements etc etc)
All techs, economy & researches treaties, bonuses (ships, bc), anomalies, different quality planets, events and megaevents can imbalance the game

The role of customized races, building, or tech trees, and what is allowed in multiplayer, or how what is allowed is determined.
a) standard rules for all

this same tech tree or different techs tree (without using abilities from other tech trees)
The role of random events in a suddenly increasingly competitive environment. Random events usually do not go over well in an environment where balance is practically the one and only commandment(second if one includes Thou Shalt not Mod, which is really just an extension of the former).
Options:
enable/disable all events
enable/disable special event
(I know that some events can strong imbalance game, but other are better for game f.e. comet give resources - asteroids.)
How an empire is managed after a player quits, whether if is abandoned and the planets made empty, the empire becomes ruled by an AI replacement, it is divided among the remaining players, etc.
a) no orders (players gives any orders)

race by controlled by high-level AI
c) race is surrendered (emperor left his kingdom) and after X turns (game option = 3, 5, more?) UP votes who can take surrendered empire.
Do you think about UP vote system in multiplayer?
1) To UP belongs all races which have "universal translator" technology (when trade and communication is possible)
2) First discoverer "universal translator" technology is president of UP* (if in this same turns, look to higher influence, if this same, look on the higher rating/score)
a) standard rule (AI decide about law proposition)

host decide about queue of law proposition (pre-game option)
c) president of UP*: all UP races votes who is president of UP for X years, and after that is re-election of president - president decides, which law is voted - new one or break existing (but cannot choose one, that were voted less than three meetings ago)
... or can build proposal of new law (but other type than three meetings ago
I hope that I helped you,
Greetings