Английский. Запуталась во времени прошлом..

Упражнения делаются не для учителя, а для своего развития. Поэтому вам надо в любом самоучителе или учебнике прочитать соответствующие темы: Past Simple и Past Continuous. В самом худшем случае у вас на это уйдет не больше часа, а польза будет реальная. В отличие от простого переписывания готовых ответов.

He had not a car, so he walked home. У него не было автомобиля, поэтому он пошел домой пешком.
He was crossing the park when he saw a little girl playing near the river - she was running after the birds. Он пересекал парк, когда увидел маленькую девочку, играющую у реки - она бегала за птицами.
The sergeant sat down to have a rest and opened his newspaper.
He was reading the sports page when he heard screams: the girl was in the water and she was waving her arms. her mother was calling for help.
Sergeant Harris ran to the river and jumped into the water.
A lot of people were watching the scene.
When they saw thar the girl was safe they all were clapping and cheering.

1.Simple
2.Continuous
3.Continuous
4.Simple
5.Continuous
6.Simple
7.Simple
8.Continuous
9.Simple
10.Continuous
11.Continuous
12.Simple
13.Continuous
14.Continuous
15.Continuous
хотя в некоторых местах и не так, в зависимости от ситуёвины, например, 14-15 можно и Simple.

А начало вопроса знакомо... Рождественский?

Я бы так сделала (не факт, что все правильно) :
1) did not have
2) walked
3) was crossing
4) saw
5) was running
6) sat down
7) opened
8) was reading
9) heard
10) was waving
11) was calling
12) jumped
13) were watching
14) clapped
15) cheered