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I found this diagram in Erdas manual. I don't know if it is what you're asking about>

For the last question check the first box in this DOCUMENT.

"Landsat TM Band Combinations 3,2,1 This RGB combination simulates a natural color image. Sometimes used for coastal studies and detection of smoke plumes. 4,5,3 Used for the analysis of soil moisture and vegetation conditions. Also good for location of inland water bodies and land/water boundaries. 4,3,2 Known as false color Infrared; this is the most conventional band combination used in remote sensing for vegetation, crops, land use and wetlands analysis. 7,4,2 Analysis of soil and vegetation moisture content; location of inland water. Vetetation appears in shade of green. 5,4,3 Separation of urban and rural land uses; identification of land/water boundaries. 4,5,7 Detection of clouds, snow, and ice (in high latitudes especially). 4-3/4+3 NDVI Normalized Difference Vegetation Index; various ratios of TM bands 4:3 have proven useful for enhancing the contrast between vegetation types." Source: http://www.sfu.ca/geog452spring01/group3/data.html