How does the death of Einstein lead to the rise of the Empire? Note that in Red Alert I, the Americans seem to be absent from the Allied forces, while Red Alert II has the USS Arizona memorial. In the original RA timeline, the US was busy fighting Japan on it's own, but in the altered timeline, the US either had to split their forces helping Europe, or concentrated their attention there. Either way, this meant the Empire had the time and space to build itself stronger.
The Empire of the Rising Sun's lack of a dedicated aircraft production structure unlike the other factions and reliance of Transforming Mecha units (Mecha/Jet Tengu, Striker/Chopper-VX, Sea/Sky Wing) for air power instead may appear odd until you realise that the Empire is based on Imperial Japan, which did not possess an independent air force and which instead maintained two air forces under the command of the Army and the Navy respectively.
Though the United States Air Force didn't achieve independent status from the Army until 1947, either, so Imperial Japan wasn't alone among the major belligerent powers in World War II for not having an independent air force. That said, the US Army Air Forces had wrested a substantial amount of independence from the Army, while its Japanese equivalents were on a much shorter leash.
The United States doesn't seem as powerful as they were in Red Alert 2. In the Imperial Campaign, Los Angeles is invaded and America is subdued as early as the end of the second act. Perhaps Cherdenko's plan did work after all, but it only hit the Americans the hardest.
That, and Ackerman is easily replaced by an Imperial android spy.
Though it's never explicited stated that Ackerman is an Empire spy in the Allied campaign, there are some subtle hints. In the mission where you take him down, the main enemy base almost always has no attack dogs, and will almost never train any. One of the major battlefield roles of attack dogs is to sniff out enemy spies; the last thing Ackerman wants are his own defenses to give away his secret.
Furthermore, if (and only if) the player trains spies of their own, they will randomly note during gameplay that Ackerman building up all these doomsday weapons right under the Allies' noses is extremely suspicious, and wonder how he was able to pull it off.
The lack of any Civil Warcraft scenarios in the main game's Imperial Campaign seems a bit odd, since even the Allies get one. But the price for treason in Imperial Japan was likely very high, and the idea of Tatsu betraying his own father likely would have made the whole ordeal even more severe.
The Mt. Rushmore mission: The President states that if his heart stops, the weapon will fire. Given he wants to fire the weapon anyway, why can't the order simply be given remotely instead of driving to the firebase, since there must be some kind of transceiver that monitors his vitals?
Because he's lying. The Imperial campaign reveals that Ackermann is a Spy Bot and clearly has no heart. The Empire probably just counted on the Allies being too stupid to realize (which is true) and made up the heart emitter thing so they won't kill their precious spy. Also, there would be massive political fallout if the Allies killed a President, so that helps as well.
I assume he was going to use the radio tower you blow up at the start of the mission, and that by destroying it, he'll need to reach the firebase to activate it personally, since the only other way to activate it remotely (his heart stops) will be to kill himself. Then again, if Ackerman was Actually a Doombot, and it was meant to use the Mt. Rushmore superweapon to level Moscow, why didn't the Empire give it the order to fake a "heart attack" to launch the superweapon?