Music Theory: Can you help me better understand Intervals and note relationships?

I have basic knowledge of building chords and intervals but one thing I noticed that is important in creating moods,melodies and what have you.. is the next interval.

Is my thinking right that if you really want to create a certain theme or mood you have to be aware of how the last note, current note and the next note you choose will make it sound like?

Like for example someone might say just play a major scale or this chord progression for lead but that gives you some range to choose from if I played for example C , B , G in that order it creates something different from G , C , B….and so on…but they are the same notes and in key.

How important is the order and space of notes?

Can you explain more to me please?

Do all intervals have THAT unique sound regardless of the key?