Are there mood or any feeling change when we shift from one major key to another and does is this related to selecting the correct key signature for a certain song or melody .
There aren't specific 'moods' for key changes, but you can make some observations about their effects.
In classical music there are common key changes and to some extent they occur in a common order. Major key compositions modulate to the dominant, then to a related minor key like relative minor, then to the sub-dominant. Minor key compositions modulate to the relative major first. Both will modulate back to the starting key for the ending. I am generalizing very broadly. There are many other designs for the order of key changes. Not following the typical design has some effect where it can be a surprise. Modulating to the dominant is described as creating tension and the final move back to the tonic key resolves the tension. Modulating to the sub-dominant has a somewhat relaxing feel. Personally I note that with these effects modulating by adding a sharp to the key (to the dominant) moves in the direction of tension while adding a flat (move to the subdominant) moves to relaxation.
Moves between parallel major/minor keys can be described as becoming happy or sad. Or, perhaps darkening or lightening. Some people think those major=happy & minor=sad associations are corny, but they are very prevalent.
Changing the key by moving a step up (Like C major to D major) gets described as adding excitement.
Generally, I think you can look at how many changes in pitch happen with the modulation and then talk about distance between the keys. So, G major (one sharp) to E major (four sharps) involves a change of 3 of 7 notes. That is fairly distant. It would create a tonal contrast.
Notice that there aren't that many specific moods like jealousy, fear, remorse, optimism, etc. As Alphonso says in his post those feelings are more likely to come from your themes - rhythm, tempo, dynamics, harmony, etc - key changes can be used to highlight or contrast these thematic changes.
Mostly the mood or feeling is created with the actual musical composition, and is not a direct effect of using a pitch change. Pitch shifting is one of the tools available for composing.
When you change keys and maintain the scale in the same composition, (move from one key of major to another key of major) you are shifting pitch, or modulating.
Shifting upwards in pitch can create a sense of excitement or urgency depending on how it is used.
Shifting downward can also invoke certain feelings.
If you are not modulating in the composition, selecting your key for a piece has many considerations, including but not limited to the instruments and/or range of the singers involved, planned modulations or relative scales you want to use, and how certain instruments sound in their ranges (trumpet and brass instruments for example).
The question of if performing a piece in a higher or lower pitch key can change the mood or feeling is a matter of some debate among musicians, and I don't believe there is a definite answer.
This question may have more information for you: How to dramatically change the feeling of a song while keeping the melody largely the same?
It just makes the song higher or lower in pitch. Every major song can be played in c major. you just modulate it to your liking.