Ответ:
№1: ........... did Susie leave home?
How long
How long ago (Сколько времени назад ... ; ago говорит нам о Past Simple)
While
№2: I don't remember....... that shop before.
seeing (remember doing smth - некоторые глаголы требуют сспользования герундия (Gerund))
see
to see
№3: His car is not..........as mine.
more modern
most modern
as modern (as ... as... устойчивое выражение используется при сравнеии, такое же... как .... )
№4: The teacher made me.............. behind after school.
stay (Complex Object (сложное дополнение) после глагола make всегда стоит глагол без частицы to)
to stay
staying
№5: We couldn 't find anywhere.............. the car.
park
to park (требуется инфинитив - мы не могли найти место, куда припарковать машину)
parking
№6: He is thinking about.......... to Spain this summer.
going (think about doing smth - Gerund)
to go
go
№7: ............. to Mike today? I need to ask him something.
Will you have spoken
Will you have been speaking
Will you be speaking (Future Continuous)
№8: He's........... the cleverest boy in the school.
far
by far (вне всяких сомнений, безусловно, несомненно; остальные варианты не подходят грамматически и по смыслу)
much
№9: Mr Johnson is regarded............. a very successful lawyer.
as (to be regarded as -устойчивое выражение)
like
so
№10: I............ my work by 4 o'clock, so I went home.
had finished (Past Perfect - действие было выполнено к опрделенному времени в прошлом)
was finishing
will have finished
№11: The weather is getting hotter and ...........
the hotter
hottest
hotter (жарче и жарче, сравнительная степень прилагательного)
№12: I haven't played tennis............... I was at school.
for
just
since (Present Perfect - используется since с тех пор, как)
№13: That was.............. party I have ever been to.
the best (самая лучшая вечеринка, на которой я когда-либо был; превосходная степент прилагательного)
the better
best
№14: My new bed is............than my old one.
comfortable
more comfortable (сравнение - сравнительная степень)
most comfortable
№15: .............. is a great way to relax.
Read
To read
Reading (Gerund выступает в роли подлежащего - чтение)
Объяснение: