yes, changing mode while still using the same "root" note will give you a different flavour. changing key and keeping the same mode will keep the same flavour, but will create a moment of transition at the point of changing key, which will have an emotional resonance. changing key and mode will do both.
all your questions could be answered by simply listening and analysing to some of the music that has been recorded over the last 70 years. rock and pop music on the whole is not particularly "adventurous", but there are some great examples out there of more sophisticated writing (abba, beatles, bacharach...the list goes on). progressive music and "classical" music will employ these techniques in abundance, so branch out and listen to some different styles.
if this was a painting forum and we were discussing painting techniques, asking what colours you should use would seem to be a bit of a strange question, wouldn't it? you'd realise that the colours you use in a painting help to express your creative intent. expert painters on the forum would probably advise you to go to a gallery and look at some paintings. compare and contrast as many artists as you can, absorb and learn. understand why they made different creative choices, used different techniques and why you have different emotional reactions to their work.
talking about music in the way we are here, is fine in certain respects, because we're getting down to the "nuts and bolts" of it, but music is a creative endeavour and ultimately is learned by doing. so write some music. see what happens when you use certain techniques like changing mode, or changing key, or both. listen to other musicians do it and figure out why it works for them in that context. steal from the best and incorporate those ideas into your own music.