in, out, on, off  are about the location of objects
Ex:I have a phone in my pocket, there's a fish on the plate
into and onto  are about movement (from out to in and from off to on respectively)
Ex:I put a phone into, I put a fish onto the plate
(more information in https://www.youtube.com/watch?v=1QFuPU47o4w)
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in to vs into
If you wish to write that you went somewhere to let a representative of a company know you are disappointed with a product or service, you can express that idea using either form. But if you write, “I walked into the office to lodge a complaint,” the sentence focuses on the prepositional phrase “into the office.” If you write, “I walked in to lodge a complaint,” the emphasis is the phrase describing the action: “I walked in.”
*'in' is part of the verb 'walked in'

On to vs onto
Onto and “on to” can be more confusing, but think of the problem this way: “She drove onto the highway” means, “She drove so that she was on the highway.(motion from 'off the highway' to 'on the highway')” Conversely, “She drove on to the highway” means, “She headed for the highway.” The two-word form is also appropriate for figurative meanings, where no physical movement or placement exists — for example, “I think you’re really on to something.”
*'on' is part of the verb 'drove on'
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onto

Rule 1: In general, use onto as one word to mean “on top of,” “to a position on,” “upon.”
Examples:
He climbed onto the roof.
Let’s step onto the dance floor.

Rule 2: Use onto when you mean “fully aware of,” “informed about.”
Examples:
I’m onto your scheme.
We canceled Julia’s surprise party when we realized she was onto our plan.

Rule 3: Use on to, two words, when on is part of the verb.
Examples:
We canceled Julia’s surprise party when we realized she caught on to our plan. (caught on is a phrasal verb)
I’m going to log on to the computer. (log on is a phrasal verb)

1. Billy, I’m worried that climbing onto that tree limb is unsafe.
2. My daughter is going on to graduate school.
3. Jose stepped down from the ladder onto the ground.
4. The magician realized one person in the audience was onto his trick.
5. After you drive five miles, turn onto Highway 280 south.
6. The Gateses have moved on to a life of philanthropy.
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onto
    1.
    moving to a location on the surface of.
    "they went up onto the ridge"
    2.
    moving aboard (a public conveyance) with the intention of traveling in it.
    "we got onto the train"
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Onto is English, whereas Unto is American English. The expression that sparked this was "climb unto a pedestal".