I was done eating

[Maybo]

I convinced myself that I was relaxing and enjoying the fresh air, but as soon as I was done eating, I returned to the library and clocked in with 10 minutes still left to my lunch break.

Source: At Home With the Horrors: 14 Tales by Sammy Scott

What's the difference between "I was done eating" and "I finished eating"? Does the former one sound informal?

 

[emsr2d2]

I convinced myself that I was relaxing and enjoying the fresh air, but as soon as I was done eating, I returned to the library and clocked in with 10 minutes still left to my lunch break.

Source: At Home With the Horrors: 14 Tales by Sammy Scott

What's the difference between "I was done eating" and "I finished eating"? Does the former one sounds sound informal?

There is no difference in meaning. However, note that you would need to use "as soon as I had finished eating" in that sentence.
I don't see the first as particularly informal.

Note that when we use "the former" and "the latter", that's all we say - there's no need for another noun after them.

 

[Maybo]

Have I understood it correctly?:

1. Amy: Have you finished your Homework?
John: No, As soon as I have finished watching my favourite TV show, I’ll do my homework.

2. Lily: When can we go?
Bob: As soon as we complete his report, we can go.

3. Daisy: Where is John?
Alex: I don’t know. As soon as he had cleaned the floor, he left.

 

[emsr2d2]

Have I understood it correctly?:

1. Amy: Have you finished your homework?
John: No. As soon as I have finished watching my favourite TV show, I’ll do my homework.

2. Lily: When can we go?
Bob: As soon as we complete this report, we can go.

3. Daisy: Where is John?
Alex: I don’t know. As soon as he had cleaned the floor, he left.

With my slight changes above, all six sentences are grammatically correct and the tenses fit.

 

[Piscean]

2. Lily: When can we go?
Bob: As soon as we complete this report, we can go.

That's fine with emsr2d2's correction. So is this:

As soon as we've completed this report, we can go.