There's no actual difference between modes and scales ... A mode is a scale derived from the original (key) scale , with the same notes and order , but with a different starting and ending point (different root).

To solo over a certain rhythm , you sould analyze the chord progression first and identify the key , check what's the ending chord is (which will be the root note for the scale/mode you'll use in your solo) , then start soloing.

Arpeggios are chords but notes are played separately , you can use them for soloing by using sweep picking technique (it's a bit advanced for only 8 months of playing)... You should learn how to build chords using triads of a scale first.