Always almost doesn't make sense. It should be almost always.

the word 'almost' is a modifier that sticks to the word after it. It only changes the meaning of the word it's linked to. It's meaning is 'not quite all'. (Think 90%) Always means all the time. (100% of the time) So almost (90%) + always (100% of the time) = (90% of the time) Hyejeong's example: my hand is almost+always red (90% of the time, my hand is red.) Compare: my hand is always almost+red (100% of the time, my hand is 90% red) Your example: Peace between longtime enemies is always almost+accomplished... Peace... is 100% of the time 90% accomplished... In this example peace is never fully accomplished, it is always only nearly accomplished. In the correct sentence peace would be fully accomplished, but not all the time.

They definitely are not interchangeable. The order is significant - the first word modifies the meaning of the second. In your sentence - it doesn't make any sense. If you take out the 'modifier' always, you end up with "Peace is almost accomplished at a cost" - which is meaningless.

No they don't mean the same thing, I think your sentence is too complicated so I'll use an example of my own. My hands are always almost red. → My hands look almost red 24/7. My hands are almost always red. → My hands are red most of the time.

No, they are not interchangeable. "Almost always" means "most of the time." Ex. She is almost always late.== She is late most of the time. "Always almost" would mean "always close to ___" or "always near being ___" Ex. Her ponytail holder is always almost slipping out. == Her ponytail holder is always close to falling out (of her hair). Generally, I don't really hear "always almost" being said. The more natural choice would be "close to becoming/being ___" or something along those lines. Neither would be logical in your sentence, however.