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In English, there is a little dot over small letters of i and j. I am not sure what that dot signifies to - pronunciation or sound.
In Gujarati, Hindi and Sanskrit languages, there happens to be dot over letters which signifies to sound "-n" for example Ganga written in either of three with dot over "Ga" alphabet sounds "Gan".
Is there any importance altogether to have such notations? Why? How do you add the same while devising grammar rules for a constructed language?
In English, the dot does not carry meaning. It's just part of the lower case letters i and j. There is no dotless base form. Note that the letters i and j aren't dotted in every font or variant of the Latin alphabet. Notably, there is no dot in Gaelic type.
Turkish, on the other hand, does distinguish between dotless I/ı (representing the phoneme /ɯ/) and dotted İ/i (/i/).
Historically, the tittle was added to improve legibility. In late medieval blackletter, the letters i, m, n, and u were basically all made up of vertical strokes, minimum basically was ııııııııııııııı. So a dot was added to i: ıııiııiıııııııı.
Dots can be used for a variety of purposes: Inuktitut syllabics (a constructed script for a natural language) use dots to indicate vowel length, while the Hebrew abjad uses them as vowel marks (niqqud), so does Tengwar. In Arabic, they are used to distinguish letters that have come to otherwise look identical (i‘jām).
Dots are an easy way to derive one symbol from another.
As jknappen has already said: it's up to you what you want to use dots for in your script or if you want to use them at all.
A thing you might want to consider is the medium your script is supposed to be written on. Dots can be easily produced with ink on paper but they are harder to carve in wood where you might want to use a short line instead. Of course, if it is meant to be mainly printed or displayed by screens, reproducibility is much less of a concern.
You are the one who constructs the writing system, so it is your choice whether you assign some "meaning" to dots.
There are constructed scripts with dots carrying some meaning:
I'm currently not aware of a constructed scripts where some dots are just part of certain letters (like in the Latin alphabet i and j) without adding information to a dotless base form.
Dots (and diacritics generally) have been used in writing systems for several reasons:
To mark vowels
In abjads and some abugidas, consonants are written as large characters, and vowels are written as diacritics around the main characters, frequently a dot or dots, but also dashes and other small marks.
One option for a con-writing system which I haven't seen before would be to swap this, and have the vowels be the main characters, and the consonants be indicated by diacritics.
Sound modifications
Diacritics are used in some writing systems to indicate some sort of sound modification, such as voicing, lenition/fortition (turning a stop into a fricative or vice versa), vowel length, or tone.
To increase the character inventory
If a language borrows a script from another language, it might not have enough characters for all of its phonemes. One common option is to use diacritics to make more characters. This is common when languages adapt the Latin script, such as in French or Vietnamese.
Or because of language change, the writing system may no longer be adequate if new phonemes arise. One option is to add a mark to an existing character. (This is probably actually the origin of all of French's diacritics.)
To improve legibility
Diacritics can be used to improve legibility, which is the origin of the dot of "i" and "j". Some languages also use diacritics to distinguish homophones.
To mark syllables
The diaereses is used to indicate that two adjacent vowels are to be pronounced separately, as in the name Noël.
This is not a complete list. The Wikipedia page for diacritics gives a thorough look at what writing systems for conlangs use them for.
