1) https://github.com/Mavigno42/ModTest/tree/master/src/main/resources/assets/modtest/lang
You need to rename that file as en_us.lang as all resources must be in lower case.
2)
Part a: https://github.com/Mavigno42/ModTest/blob/master/src/main/java/com/mavigno/modtest/tileentity/base/TileEntityBasicInventory.java#L15
You don't need implements ICapabilityProvider, TileEntity already implements that interface.
Part b: https://github.com/Mavigno42/ModTest/blob/master/src/main/java/com/mavigno/modtest/tileentity/base/TileEntityBasicInventory.java#L17
Pretty sure you can't create the ItemHandler like this, as the SIZE value is coming from the constructor, but at the time that this field is initialized, the constructor has not yet been called.