親しい – there’s intimacy/closeness in parent-child relationships, usually. That aside, you could also tell yourself that you’d best be able to ‘see someone’/‘look someone in the eye’ (見) if you want to be close to them
新しい – the axe radical, which has been mentioned above. When you cut into something, a new surface appears. That aside, there’s 斬新 (which uses the axe radical twice, even if it’s an unfamiliar word for you), which means ‘original, fresh, completely new’. You’ll notice that 斬 is one of the possible kanji for きる, and that it’s also the kanji for ‘beheading’, so the metaphor of ‘cutting creating newness’ can be carried pretty far. Imagine it as something like ‘making a clean break with the old’, if you like.