Yes, and there's a bit of self perpetuation to all this. Because Veda have more information their picture of you is more complete and hence many credit providers are more likely to go to them for credit information. Because there are more applications going through Veda they will continue to have more information.
Ended up not getting any. 
Prepaid and Postpaid are different, the credit reporting provisions definite credit as anything where there are greater than 5 day payments terms. So if you are on a postpaid plan they have a right to check your file, and if they do a check it will be recorded!
If you are talking about the Credit Reporting Agencies, no they wont share any real details of how they calculate the scores beyond a high level description of the factors. But even if you are getting a phone and plan, the total credit amount is relatively low (e.g. say 1000 - 1500) vs. the 20-30K+ limits some have on Credit Cards so yes, I would think the impact is relatively minor.
This credit score "black mark" you talk about isn't about the application for a relatively small amount of credit, it's about the fact they now have a default recorded against them for failing to meet the required payments. Yes, even a relatively small debt is important if you have a demonstrated unwillingness to pay it. You may not like this but the evidence is pretty strong that if you won't pay small debts you also won't pay big debts (conversely if you have a history of paying big debts - ie mortgage payments, you are a good credit risk).
