Şimdi çalışmak zorundayım.
Şimdi çalışmam lazım.

Same meaning, different usage. By the way, "zorunda" sounds more "an obligatory comes from a higher authorithy"

I need to work: Çalışmam lazım or Çalışmam gerekiyor or Çalışmalıyım

I have to work: Çalışmak zorundayım

If this is a work that your boss is near to you and observes always you, so you have to be there and have to work. Here, zorunda is good.

But if this is a study, and you need to study to graduate the school, then it seems more "your choice". Then you may say: I must study. Here, both zorunda and lazım sounds good.

Çalışmam lazım=Çalışmalıyım.(I must/should)
Çalışmak zorundayım.(I have to)

you should use question suffixes "mi"(sentence suffix, not word suffix).

+Türkçe çalışıyorum.
-Hâlâ mı?
+Evet...

-Yemek yapıyorum.
+Hâlâ mı?

I said,

mutluydum

y is not buffer here

y is here the changing of "i", in "idi"

araba+ydı
Look at the last LETTER of "araba", it is a VOWEL. We add "idi", and i changes to y, and there is the vowel harmony:
araba+idi= arabaydı

ev+di
Look at the last LETTER; it is a CONSONANT. so we add "idi", and i goes to the heaven. and there is the vowel harmony:
ev+idi= evdi

But in verbs, it is not the adding of "idi". it is completely "-di" suffix. "-di" suffix is not "-idi". So, there is no "y".

gör+dü
bak+tı
izle+di
yap+tı
uç+tu

...koşmadan hoşlanıyor...
seems ok but it may mean also: "he likes without running"
(due to your expression on practical usage)