Take a look at this site. This is very helpful. http://www.vocabulix.com/conjugation/German-Verbs.html. Type any word 'lernt' and click 'search.' And the click 'Show All' for 'Present.' You will find what to use and when.
Grammatical gender is not the same as 'natural' gender. The gender of the word does not always correspond to what you think the gender of the thing should be. It is important to learn the gender of each noun and try not to make it 'male' or 'female' in your mind - as Vreny says it is not logical.
Das Kind/ the child is neuter because it is not depending on the gender but only on the age if somebody is a child. If you refer on the gender you say Mädchen (girl) or Junge (boy). But in German the gender is not always logical. For example die Sonne (sun) is female but der Mond (moon) is male. I hope it is understandable what I was trying to say...
Yes, "die" are used for all plurals, whether the original noun is masculine, feminine, or neuter. For example:
der Mann -> The man die Männer -> The men
die Zeitung -> The newspaper die Zeitungen -> The newspapers
das Mädchen -> The girl die Mädchen -> The girls
Note however, the gender of plural noun is still the same as the gender of the corresponding singular noun; it is incorrect to say that pluralizing a noun turns it into feminine as some would say. This misconception could lead to issues with understanding the declension of adjectives later on.