Premise:
OTL, Dissatisfaction with their gains in the post first Opium War Treaty of Nanking did not result in Britain finding a casus belli (October 1856) until the Crimean war was concluded (February 1856).
By then:
a. The French had aided the Qing to retake Shanghai from the Triads (September 1855)
b. The Guandong provincial government had crushed the Red Turban Rebellion (and carried out a purge of original Taiping movement extended family members and associates- 75,000 summary executions) (AUgust 1856) Notably, the governor asked for British help in the endeavor and was refused.
c. The Taiping Northern expedition had been defeated (March 1855).
d. A disfavorable opinion of the Taiping had pretty much been formed by French and British authorities (Mid 1855).
e. The Tianjing incident had taken place, crippling Taiping credibility and eliminating Yang's relatively realistic (if manipulative and Machiavellian) counter to Hong Xiquan's batshit crazy fanaticism 9October 1856).
f. The Russians had been alienated from directly joining Anglo French efforts and instead played a double game, trying to trade arms and instructers for Qing cession of the Left Bank of the Amur (they were rejected until the very end). Notably, they had begun making incursion into the Amur lands as early as 1850, and only put their efforts to a temporary halt in 1854, when word of the Crimean war reached the Far East.
Suppose the Crimean war is butterflied away (or is delayed. or occurs earlier, say in 1848).
1. How much earlier is the Second Opium war likely to break out?
2. How aggressively is Muravyov likely to pursue territorial aggrandizement in The Amur lands absent the Crimean war?
3. Are such incursions likely to spark a war and/or border skirmish is Muravyov:
3.a. simply colonizes the territory (setting up forts/settlements) while ignoring Qing admonishments?
3.b. Orders Qing officials and soldiers out and they submit? Resist?
3.c. launches premptive strike on his own initiative (without orders or preapproval from St Petersburg?)
4. Given the answer to #c, how many Qing resources are likely to be diverted from repulsing/ pursuing/ besieging and destroying the Northern expedition?
5. Is a British capture of Canton at the height of the Red Turban Rebellion (And Shai Daki's conquest of neighboring Jianxi and linkage with the Red Turbans) likely to result in an anti-Qing regime in Guangdong?
6. How long can the Triads hold out in Shanghai if the French don't help the Qing against them? Can they expect aid from the Anglo-French in case of an Anti-Qing War?
7. Is Yang Xiuqing likely to be able to form an alliance, dejure or defacto with the Anglo-French if he is effectively in charge when the second Opium War breaks out. How "Realistic" is he likely to be regarding concessions to the Brits on what they care about most?
8. If Taiping are holed up in Tianjin (rather than being repulsed from it into Shangdong) when war breaks out and develops how aware are the Anglo-French and/or Russians likely to be of this, and how will it factor into their war plans?
9. Is Russia likely to join Britain in open war against the Qing if efforts to secure the Amur "Peacefully" are rebuffed?
Technical question : What were the communication lag times between London, Paris and St Petersburg to the Far East?