That'll be algae then! Nothing to worry about, if it starts to overwhelm the plants then it is worth telling us more about your tank:
Lighting type and wattage
Tank size
Gravel/substrate type
Plant types and quantities
Fertilisation routine (including CO2 if relevant)
Water change routine
Depends, often in new tanks you get a few algae's showing up until things stabilise. Unless yuo have more than 1 watt per gallon of light and use CO2, the dosage rates on the majority of aquarium plants fertilisers are fine providing you have a reasonable plant load.