All answer words contain the given number of I's

One I

-1. Name of the first Mogwai in Gremlins (5)
-2. Chess opening (6)
-3. Singing deadly enchantress (5)
-4. Brad Garrett portrayed one on Finding Nemo (10)

Two I's

-5. Ape (5)
-6. Fill with an exalting influence (7)
-7. Bird that symbolizes the Egyptian god Thoth (4)
-8. Adore (7)

Three I's

-9. Buzz Lightyear goes beyond it (8)
-10. Responsibility for a debt (9)
-11. Camping area with no amenities (9)
-12. Surrounding area (8)

Four I's

-13. Quest (11)
-14. Acquaintances (13)
-15. Taskmaster or tyrant (14)
-16. Self-consciousness (10)

FIVE I's

-17. Traits that make people different from others (15)
-18. Rudeness, bad manners and disrespect (12)

8. idolize

7. ibis

18. incivilities

5. mimic

5. mimic

17. individualities

Hi Cue.

7.Ibis

3. siren

Great solves!

Haroula, Jema beat you to that one. Take another if you like.

2.Gambit

14. familiarities

9. infinity

A good triple!

16. inhibition

4. Pufferfish <`}}}}><

13. inquisities

1.Gizmo

15. disciplinarian

Figures that you'd get the fish answer, Koala

Joan, Chery, Haroula, Koala

Gerry, you're very close.

10. liability
12. vicinity

6. inspire

Good solves Joan and Michele

Hints for the rest of them.

11. primitive
13. inquisition

Excellent!