Yeah they are good to learn. When someone refers to the Ionian mode, they mean the major scale. Which is the most beneficial thing you'll ever learn on guitar. You'll probably learn the minor (Aeolian) next, then harmonic minor and melodic minor before you learn the other modes. Depends on the teacher, but that is usually the order. The more scales you know and the better you understand them, the more riffs and stuff you'll be able to create.

A key is the root of a song. Say a song is in C major, that means the songs is relatively circled around the note C. And it just sounds major cause of the chords that the song is made up of. Yeah if you play the Ionian starting on A, A is major. Here's the chords that exist in that scale/mode.

A major / B minor / C# minor / D major / E major / F# minor/ G# diminished.