Learn English – The use of the gerund after ‘of’

The title of your question, as well as the two sentences you present, have many problems, only some of which involve the usage of the gerund or the preposition of. We can try to correct the mistakes and to answer the question you pose, which is:

Is it correct to use preposition "of" in the sentences bellow?

Also, since the question is entitled "Using of Gerund," we assume that you want to use a gerund in your sentences.

Before proceeding, though, it's important to point out two things. First: Nothing will mark you so plainly as a non-native English speaker as misuse of, or omission of, the articles. Second: One little letter can make one big difference. Below is an adverb which here would mean at a later point on a page or in a text. Bellow is a verb which means to emit a hollow, loud, animal cry, as a bull or cow. Spelling matters!

Thus, the title of your question should be at least Using of the Gerund, and properly Usage of the Gerund; and your question, with corrections, is:

Is it correct to use the preposition "of" in the sentences below?

Your first sentence has the pronoun her in the middle of the gerundive clause "being so fussy," when it belongs instead after the preposition of which it is the object, which is of:

It's not a little unpleasant of being her so fussy.

To express this thought in the same words while using the gerund, we might try this:

It's not a little unpleasant of her, being so fussy.

This is mildly colloquial but grammatical. It would not sound out of place in conversation among native speakers, but would rarely be heard. If we dispense with the dummy "it", we can do perhaps a little better:

Being so fussy is not a little unpleasant of her.

In your second sentence, you have misspelled awful. It is not uncommon to see this word spelled with two Ls even among native speakers, to whom it may seem a natural back-formation from the adverb awfully. So, with this correction, you have:

It's awful of him having done this.

This sentence, like the first, is mildly colloquial if we add a comma, but it would almost never be seen or heard from a native speaker in this form:

It's awful of him, having done this.

If we provide the dummy "it" with an antecedent, the sentence is slightly improved while still preserving the gerund and of:

It's awful of him, his having done this.

The answer to your question, then, is Yes: it is correct to use the preposition of as you have done, but only if the sentences are properly formed. However, in natural speech, neither thought would commonly be expressed in this way. Instead, you might hear neither the gerund nor the preposition:

1. It's not a little unpleasant that she's so fussy.
   
2. It's awful that he did this.