$1.$It's the first time Hoa has cooked.

$\rightarrow$ It's the first/second/third time + S + have/has + $Vp2$
$\rightarrow$ Dịch : Đây là lần đầu tiên Hoa nấu ăn

$2.$In spite of the cloud,they took photos

$\rightarrow$ In spite of = Although: mặc dù

$\rightarrow$ In spite of/Despite + N/Ving
$3.$Because of Lan's tiredness, she didn't come to Hoa's birthday party.

Hoặc Because of being tired, Lan didn't come to Hoa's birthday party.

$\rightarrow$ Because of/Due to/Owing to + N/Ving : bởi vì

$4.$After she had cooked, she watched TV

$\rightarrow$ Thì QKHT dùng để diễn tả $1$ hành động xảy ra trước $1$ hành động khác trong quá khứ trên cùng $1$ thời điểm nói

$\rightarrow$ After + S + had $Vp2$, S + $\text{V2/ed}$

$5.$She asked Mai not to tease dog.

$\rightarrow$ ask/tell + sb + (not) + to Vinf

$6.$She asked me why she hadn't gone to work the day before.

$\rightarrow$ Câu giả định(SUBJUNCTIVE) :

S + asked/told + sb + Wh-questions + S + V(lùi thì)

@linanguyenpham