Here are some ideas for planning for the war. It is a bit rough and ready, but if you like it, it can be refined. It builds on stuff already said by many people, including the excellent analysis by Fetch.
Obviously first priority is defence. I think archers would be most useful (we've got quite a few axes already). I don't think Germany has many mounted units, so I don't think spears will be all that useful. Once we've got some more archers, I think crossbows will be good. I'm a bit undecided between horse archers and war chariots. HA are stronger, but a lot more expensive. A few HA or WC behind the front line gives us mobile reinforcements plus some scouting/pillaging options.
I think we should switch research to construction (7 turns) then back to optics. I think catapults will be very useful if we go offensive.
I think we should give Philosophy to Peter in exchange for declaring war. It will give Bismarck something else to worry about and stop him concentrating everything on us. However, I think we need to be careful about how far we trust Peter - I would not plan to strip our defences along the border with Russia.
Here is a city-by-city analysis:
Frontier cities
Build defence in these cities asap. Also, build slower moving units here cos they don't take as long to get to the border.
Basillica
Will finish Barracks in 5. Then build archer (5).
Switch citizen from 1NE(3F1C) to 1SE(1F1H1C).
Send worker to Const Falls to help chop forest.
Keep axe, archer and send war ch. to do some careful scouting.
Build queue after 10 turns: see if we still need urgent defence (archers) or can start on crossbows (10) or cats.
When have some extra archers from other cities (or from what is built here), send a couple of them to guard the iron.
Toot Uncommon
This is some way from being war ready.
Could switch to Barracks (18) followed by Aqueduct.
If any workers spare, use to chop jungle and build mines.
Const Falls
keep building forge, but when it will only cost 1 pop, use the whip (we already have 1 citizen refusing to work, so we won't be any worse off, and we can view the whip as an
encouragement to get back to work). This means it will take about 11 turns to finish.
Russian border cities
These cities should not be left undefended or we might get a nasty surprise. The urgent problem is Germany, so I've not proposed any increase in defensive levels.
Fort Impervious
This is meant to be a GP farm, so leave alone.
Keep 2 axes, though if an archer arrives (maybe from Mic Gate), then keep archer and send 1 axe to German front.
New Port City
NPC is lacking production and is not really going to contribute to the war effort.
Once worker finishes, build market.
Keep sword and spear, though if get an archer, send sword to front.
Cities behind frontier
These are a bit of a mixed bag regarding the war effort. Ideally, they should be supplying reserve troops, but I can't really see it. I'm not quite sure what we should do with the economy - I've made some suggestions for increasing production (in one case by helping the pop increase along the way), but if we need cash then we'll have to forget it.
Old Sarai
OS is some way from being truly productive and I think it needs more pop. Therefore I suggest switching to Granary (13).
Switching a citizen from 2W1S (2F1H) to 1E (1F3H1C) temporarily slows growth but give Granary in 10 and adds 1 commerce. If we can afford to lose 1 C overall, we could switch 1S (2F3C) to 1W (3F1C) to regain the food we lost.
Once Granary completes, we should see how the war is going. If we are in desperate need of troops, I suggest going for Barracks, otherwise back to forge.
Auda City
This is not a production city, so I don't recommend building war units.
If we can afford to lose 2 commerce, I suggest we switch a citizen from 1W2S (3F2C) to a Scientist cos the city is likely to grow and become unhealthy before the aqueduct finishes.
If there are any workers spare, they could chop to hurry the aqueduct, but it is a low priority.
Keep 1 archer, send 1 to Toot Uncommon and 1 to Basillica.
Abydos
Abydos is almost ready to start churning out units.
Leave forge (1) to complete, then build archer (5), not market.
Switch citizen from 2N (2F1H) to 1E2S (1F2H) to prevent pop growing and becoming unhappy.
Archer would be built in 4 if we did this.
Once forge is built and with extra hammer, axes should build in 4 and archers in 3. Could build a couple of each (or cats if we get construction), then go for crossbows.
Keep 1 archer, send 1 archer to Old Sarai, send 1 warrior to Basillica, send sword north of city border to Basillica.
Northern cities
These are more distant, so I recommend building units like horse archer that move faster. However, Mic Gate is ready to go, so we should probably pump out an archer or axe or 2 immediately.
Boaring Wallow
Leave forge to complete (20).
After growth in 15, siwtch to working more hammers and less food, otherwise city will be unhealthy when forge completes.
Chop some forest to hurry forge. Once it completes, then can switch to crossbows or horse archers.
Keep both warriors.
Micalian's Gate
Switch build to archer (4). Then build more axes and archers if defence still required, otherwise go to horse archers (or war chariots). One possibility is to build a couple of archers to send to FI and NPC to free up their axes.
Send exiting archer to Basillica, and keep one of the archers that gets built.
Overall
I think the biggest problem is if Bismarck sends a Stack of Doom which will arrive in 5 or 6 turns. Then I think the 3 frontier cities will have to support each other with reinforcements arriving from cities further back. We'll probably have to live without pillaged resources for a while. I think we need to War Chariot on the border to be in a position to give an early warning.
Once we complete the next turnchat (or the next 10 turns at any rate) and we have followed a plan (even if it is not exactly the one above) that gives us a boost in units then I think Bismarck should find our defences hard to break down. The power graph shows we can compete with Germany when we try and if Peter at least keeps a few German troops occupied we will effectively have a lead.
This should allow us to consider an attack for the TC afterwards. Intelligence showed us that Berlin had an axe, a spear and 3 archers - most with promotions. My experience of wars in Civ 4 is that we can break that down, but we'll probably lose quite a few units trying. I think that is a good argument for cats and possibly a few suicide axes as well.
From what I remember of Hanover, it had very poor defences. It also appears to have quite a lot of culture, so I think it could be worth taking as well.
Anyway, I hope this helps.