Learn Russian: Мы должны генерировать новаторские идеи.

The word должны acts like a short-form adjective agreeing with the subject мы, and it carries a strong sense of personal duty or obligation (we are obliged to). Using нам нужно would simply state that a need exists for us, which sounds less like a direct professional mandate.

Is генерировать an imperfective or perfective verb in this sentence?

Like many foreign loanwords ending in -овать, генерировать is a biaspectual verb, meaning it can serve as either aspect. Here it acts as an imperfective verb because the generation of ideas is framed as an ongoing, continuous process. If you need to emphasize a single, successfully completed result, you can use the explicitly perfective prefixed form сгенерировать.

Why doesn't the adjective новаторские change its ending for the accusative case?

Because идеи is an inanimate noun. In the plural, inanimate accusative nouns and their modifying adjectives look exactly identical to their nominative forms. If the noun were animate, the adjective would have taken the genitive-looking ending -их.

How would we modify this sentence to say we need to generate 'different' ideas using the pronoun иной?