Learn Finnish: Eikö kohdemaan uuteen arkielämään ollut vaikeaa tottua? - Was it not difficult to get used to the new everyday life of the host country?

This is driven by the verb tottua (to get used to). In Finnish, verbs describing becoming accustomed, acquainted, or emotionally attached to something govern the illative case. You are grammatically getting used into the new everyday life.

Why is vaikeaa in the partitive case instead of the nominative vaikea?

When an adjective describes an infinitive verb (here, the action of tottua), it must be in the partitive case. Because an action is abstract and uncountable, Finnish treats it like an uncountable mass noun, requiring the partitive vaikeaa.

Tottua is at the very end of the sentence. Is this the standard word order?

It is common but not strictly required. A more neutral, textbook word order would be Eikö ollut vaikeaa tottua kohdemaan uuteen arkielämään? Placing the infinitive at the end wraps the sentence around the long noun phrase, which is a very natural conversational flow in Finnish.

Why doesn't kohdemaan match the illative case of uuteen arkielämään?

Kohdemaan is the genitive form of kohdemaa (host country). It acts as a possessive modifier meaning 'the host country's'. While adjectives like uusi must agree with the noun's case (uuteen arkielämään), genitive modifiers stay in the genitive no matter what case the main noun takes.