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Are the tenses correctly used at points 1-3? - Yes - 2 and 3 especially are perfect.
Is it possible to use "was playing with it"? - Yes, and that's the change I suggested :)
Is it possible to use "disintegrated" instead of "has disintegrated"? This is related to your other two questions.

Yes, realised and have realised, found out and have found out, all of these are possible. "has realised" is the present perfect tense, and you'd generally use it when you want to emphasise that a past event has present consequences.

So: if you are talking about something that happened *entirely* in the past, you would not use present perfect. Last week I stepped on his train, then his brother disintegrated it. When we went to the shop, I realised she has good taste in clothes. Two weeks ago I found out about his criminal record, so I fired him from my company. Present perfect is impossible in these sentences.

If you want to emphasise that a past event has had lasting consequences that are still relevant in the present, you might use present perfect. His brother has disintegrated it, and it's still in pieces now. I have realised she has good taste in clothes, so I'm going to ask her to choose an outfit for me. I have found about his criminal record, and I intend to fire him.

I think often present perfect is unnecessary, you can use simple past and it's grammatical. It's just a question of what you want to emphasise. In every sentence I suggested here, you could use simple past and it would be fine. It's difficult to describe precisely when it *is* necessary!

One general case where it's necessary is where if you used past tense, the listener would think that meant the situation was somehow *finished*. Examples from wikipedia are "He has written ten plays" and "They have never travelled abroad". If you said "He wrote ten plays" or "They never travelled abroad", the listener is likely to think that the people you are talking about are now dead.