Narau (to learn) *We often say "to learn" benkyou suru and I would use "benkyou suru" for this title. 

Konnichiwa.

Watashi wa kyou takuasan naraimashita tta kyo ni deshita.

*"naratta" is the past form of "narau" and the polite form is "naraimashita". "deshita" is the oast form of "desu". 

I would say: Watashi wa kyou, takusan benkyou shimashita. 

Watashi no sensei wa ii sensei (or ii hito) desu. Kare wo ga sonkei shimasu desu.

"sonkei suru" is a verb which means "admire / respect" 

Watashi wa ureshii desu. --> Perfect! 

Sayounara.
(Can I use ja ne here?) --> "jaa ne" sounds casual, so, in this note, I would say "dewa mata" and it's better to use it instead of "Sayounara". I think we don't use "sayounara" very often in our everyday conversation, at least I don't. 

Hi, great job! Please get accustomed to the Japanese sentences. Sometimes the literal translations don't sound natural. I hope my English isn't bad and this helps you.  

Time comes first in Japanese, I think you mean takusan? And since it has a verb you don't use desu, and instead add 'mashita' to the end.

Kyo watashi wa takusan naraimashita

Watashi no sensei wa ii desu. Kare ga jouzu(skilled)/sugoi(awesome) I think is better. I'm not sure what sonkei means. Although it might be right, a Japanese person would be better explaining adoration. 

You also don't need to keep using watashi wa. Once you've used it once, it's understood that you're refering to yourself. Although if those are just three separate unreladted sentences then it is fine.

And I don't yet know how to sign off in Japanese :p Maybe mata ne~(until later)

Hope that helps. :)