Hey Harvester,
Diplomacy stuff has been brought up quite a bit, and Ironclad has said they're going to keep improving it. In reference to some of your points/questions:
The computer just spams me with missions to "destroy XXX of the XXX". Heck, I get missions even if they are civilizations with whom I have no contact.
Contact is handled a bit differently in Sins than in some games. In Sins, as long as you have "seen" an AI's ship (even a scout), you're considered in contact and the AI can start giving you missions. I've been able to postpone getting a lot of missions by just being a bit more conservative on early-game scouting.
I have no way to forge alliances based on proximity, strength, revenge, etc. The game just cruises along spamming me with endless missions that I can't complete. Of course, during the course of the game I will complete various missions based mainly on luck or my own personal goals, and I may get a few alliances, but I don't really have any control over any of it.
All the AIs give you missions. Combat missions are only given if the target AI is within 2 jumps from any one of your planets (sadly, jumping from star to star counts as one jump, and that does lead to some difficult to finish missions). If you scout and see which AI is close to you, it possible to focus on doings its missions so you can get that cease fire going quickly - I tend to do this a lot, always trying to keep only one flank open to the enemy. Likewise, the AI also has its goals, and not all of your allies will be its allied and it can ask you to destroy ships/buildings of your ally

I have no way to ask another empire to do my bidding. Why can I not offer a mission to another empire to attack so-and-so and I'll pay them?
Once you have a peace treaty with an AI, you can select its units (by clicking the pip bar around a planet, for example) and on the UI bar where normally your unit commands are there will be options to tell the AI to attack, defend, or I think move to the target of your choice. They're pretty decent about doing it, but they don't always drop everything to do it ASAP (and may refuse if you want them to attack their ally). You don't even need to pay them

The rest of your suggestions I can agree with - most of them have been brought up previously so hopefully we'll see them down the road. I particularly would like being able to freely offer the AI some resources for a bit of happiness (like if I just need that 5 or 10% and don't want to wait for a random mission), and it would also be great if you could ask the AI for some resources when you're in a pinch

One of my early suggestions was to tweak diplomacy a bit so that same-race AI would be a bit easier to please than hostile ones. The game's background is that the TEC is bitterly at war with the Vasari and Advent, so to me it would feel more contrived if they just started neutral/friendlyish based on proximity alone. I think it'd be cool if all the TECs found it easier to get along, all the Vasaris, etc. It would play more into the background lore, and you could justify spending more effort to ally with hostile races for joint attacks, because you'd have abilities from two different races at your disposal than just more of the same one