"Information" is uncountable in English, so you treat it as "it".
Some information is missing.
A lot of information is missing.
A piece of information is missing. (Yes, you can change this to "Many pieces... are...")
It's a lot trickier with "data", as this is technically the plural form of "datum". You would definitely make this distinction in a technical/academic context. I had a quick check of how often "is/are" is used with "data", and "data are" is still use much more often than "data is", although "data is" seems quite acceptable. I'd do a search on the phrase you want to use, to see how other writers have managed it.