this question is for those who have communicated/invoked with entities and gods.
Why are you interested in us and in the cooperation?!
Was there a moment when they tried to convey the truth to us that we are most likely their children?!
are they allowed by free will to enlighten us why we are here on earth?!
Do they spontaneously visit us or others without our rituals/approval/attention?!
Genuinely the reasons why depend on the entity/entities.
The only other question I can answer is your last one which is yes they can and do interact spontaneously.
?
Why are they interested in us? Depends. Some have their own agenda. Some will seek you out specifically. Most of the time, people simply call entities and ask for their powers to aid us. Doesn’t necessarily mean you’ll develop a strong relationship with them, but you can call on whichever entity you wish at any time.
Imho we’re all part of the same divine Source, so I don’t really buy into the “child of/spouse of/incarnation of X entity” thing, although if other people believe this, who am I to tell them they’re wrong?
Sure, nothing prevents UPG
Yep, I’ve had multiple entities seek me out when I had no idea who they were and/or no particular interest in working with them, and developed good relationships with them over time.
Secrets from the Veil 
It varies from person to person. For me, it was the ancestral connection. Freyja was my matron. She helped me understand “the point” telling me for years, “In time all will be revealed”
That’s for us to find out. Someones reasoning for being on earth is their own reasoning. I know I stay in the reincarnation cycle so I can destroy the status quo. Call me a boddhisatva if you will. I am not a spiritual teacher however and I do not claim to be one.
Couple nights ago Odin visited me spontaneously. He wanted to channel through me. Called me Ymir. Told me to never lose sight of who I am and why I fight.
Freyja in every regards is my aunt. The Clan MacLeod are said to be the children of Frey.
The answers vary from entity to entity and from reasoning to reasoning. That is what makes it fun.
I believe, 100%, that there is mutual gain in most interactions, though those benefits may not be obvious to us.
I’ve definitely been treated like a child on more than one occasion, but not treated as an entity’s child.
In my experience with my patron, there is some set of rules that they have to abide by when sharing hidden knowledge, even if it’s just an unspoken rule. (Though this is UPG from my first-hand experience and should be taken with a grain of salt.)
This really depends on the entity. If there is something that someone needs from you, then yeah they may reach out, but I am always cautious about things that reach out to me first, because I’ve had quite a few experiences with parasites in the past that just “show up and need something from you.”