Learn Russian: Этот странный аппарат — новое изобретение. - This strange apparatus is a new invention.

In Russian, the present tense of the verb "to be" (am, is, are) is almost always skipped. When a sentence links one noun phrase directly to another noun phrase (like saying "X is Y"), Russian uses a dash to take the place of the missing "is". Here, it connects the subject (аппарат) to what it is (изобретение).

Why do the words describing the nouns have different endings (Этот странный vs. новое)?

Adjectives and pointing words must match the gender of the noun they describe. Аппарат (apparatus) is a masculine noun because it ends in a consonant, so it takes the masculine forms Этот (this) and странный (strange). However, изобретение (invention) is a neuter noun, so it takes the neuter adjective ending -ое, giving us новое (new).

If I wanted to change this to "This is a strange apparatus, which is a new invention", how would I use который?

To add "which" (который), you must match it to the gender of the noun it refers back to. Since аппарат is masculine and serves as the subject of the new clause, you use the masculine Nominative form который. The sentence would become: Это странный аппарат, который — новое изобретение. (Notice we also changed Этот to Это at the start to mean "This is a...").

Why does изобретение end in -ие? Is that a common ending?