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3. Eorum amicitiam confirmare voluit quo facilius Romanis bellum inferret.

My translation is:
He wished to strengthen their friendship with which (or so that) he made war with the Romans more easily.

The meaning of the sentence is clear. But I wonder why here quo instead of qua is used. After all, amicitia is feminine.

'quo' might be referring to the sentence, i.e. the statement as a whole, whereby the relative naturally becomes a neuter.

Thanks timeodanaos!

This is also what I suspect. But on the other hand, would it also be correct to use qua?

Quo is regularly used to introduce clauses of purpose that contain a comparative (in this case facilius). You can think of it as 'he strengthened the friendship the faster to make war.'