it is very helpful to learn Kanji from this lessons

is this the right word

Is this word correct? The pronunciation character above the character is "go," but it is being pronounced "ka ta i" from what I can hear. 

It's correct. Kanji often have at least two readings.

He's saying the kunyomi かたり which means 'a talk'. Think of the monogatari light novels and anime series.

The onyomi you can find in compound kanji words such as 日本語 （にほんご）which means 'Japanese language'.

It's correct.....

If you check the Japanese for other Languages, you'll find that just by adding 語 after the country name, you'll get the language of that country (for most cases)

i.e. Country Name (Japanese) + 語 = Language.

e.g. 日本 +語 = 日本語 (Japanese);

        スペイン + 語 = スペイン語 (Spanish) etc.

Note: There are some exceptions like, English : 英語.

It's correct.....

If you check the Japanese for other Languages, you'll find that just by adding 語 after the country name, you'll get the language of that country (for most cases)

i.e. Country Name (Japanese) + 語 = Language.

e.g. 日本 +語 = 日本語 (Japanese);

        スペイン + 語 = スペイン語 (Spanish) etc.

Note: There are some exceptions like, English : 英語.