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. Sign of rank, title or award (8)
-10. Responsibility for a debt (9)
-11. Camping area with no amenities (9)
-12. Surrounding area (8)
-13. Restrain (7)

Four I's

-14. Extended period of questioning (11)
-15. Acquaintences (13)
-16. Taskmaster or tyrant (14)
-17. Self-consciousness (10)
-18. A word in the US pledge of allegiance (11)

Five I's

-19. Traits that make people different from others (15)
-20. Rudeness, bad manners and disrespect (12)

2. gambit
18. indivisible

5. mimic

13. inhibit

Hi Cue.

4 - puffer fish

20 - incivilities

19. individualities

8. idolize

I say, you're right on the money!

3. Siren

9. Insignia - Hi Cue

Bernie

14. inquisition

17. inhibition

7. Ibis

16. disciplinarian

1 - Gizmo

7 - Ibis

Your I's are on target

Hi Bernie

15. familiarities

6. inspire

10. liability

12. vicinity

Hi Cue. No.11 is too tough for me.

11. primitive

You must not be a camper, Remi, but it looks like manxman might be

Good finish, guys