I'm especially not sure about 気にかかる. for 気にする and 気になる, I think the difference is that 気にする is ''negative'' only while 気になる can also have a positive meaning?
- ～が気になる: Intransitive. One passively gets worried or interested due to some external cause. It can be positive ("be interested in", "be curious about"), or negative ("be disturbed by", "be worried about").
- ～を気にする: Transitive. One voluntarily/actively cares for, or worry about something.
- ～が気にかかる: Like ～が気になる, but has a negative tendency.
- 新型のiPhoneが気になる: OK. You're interested.
新型のiPhoneが気にかかる: May have a negative nuance. (You're worrying if the new iPhone has some problem? Or thinking about the new iPhone is not good for you now?)
- 病気の友人のことが気にかかる: OK.