Is there any difference between "I eat" and "I do eating" ?

If they are, what would they be?

Alex is correct about inserting do for emphasis. However, when we do that, we use the pure infinitive eat rather than 'eating'. "I do eating" is totally incorrect.

However, if you are taliking about classes or activities, you can rather informally say things like this.

eg I do dancing on Wednesday evenings, and I do swimming on Saturday mornings.

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If you insert do between the subject and the verb you make the entire expression a bit stronger."Do" is often used to emphasize and to stress a certain meaning.The continuous form "eating" indicates that you are eating at the moment.
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I eat