Likewise solfege/sight-singing: that's an invaluable tool, but it takes quite a while to truly do it well. That would likely help more than transcribing. By "quite a while" I mean something on the scale of several months of intensive practice.
Yes, do this. It requires a lot of work to get to the point where one is proficient, yet it becomes very rewarding when one can apply the skill. It teaches you to internalize pitches, internalize the construction of a scale, internalize a concept of harmony. It takes you from merely recognizing pitches to internally generating them. It is like the difference between taking a guess on a multiple choice question, versus identifying the answer before reading all the possible options.
Start transcribing simple singable melodies (emphasis on singable). Things like nursery rhymes, folk songs, hymns. To the melody you can add lead sheet chord symbols for harmony.
Following that, work on multiple melodies at once. A good place to start is with hymns, transcribing the soprano and bass parts. Once you are comfortable with two outer parts, try adding the middle voices, alto and tenor.
Take a melody and harmonize it yourself. Start with simple I, IV, V chords. When you are comfortable with that, expand your use of chords.
Take excerpts of orchestral scores and transcribe for piano solo, or 2p4h, without the use of software aids. This will train you to write for piano when the music you are transcribing is not originally for that instrument. Play your transcription at the piano and ask yourself: does it feel manageable in the hands?
Transpose. Do this with all exercises above. A good starting place is +/- three sharps/flats, eventually expanding until you can transpose to all 12 keys. Both on paper and at the keyboard, but without using software aids. Keyboard transposition would preferably be either from memory, or sight transposition, that is looking at the score in original key and playing in transposed key.
One thing which I found very helpful was improvising. When you improvise, over time, you develop a kind of symbiosis with the keyboard where you can hear something in your head and mimic the idea physically. I found this to be immensely helpful.
Yes, do improvise and work out ideas using the keyboard.
May i know which songs and sheet music i can refer to to start with for beginning maybe for the five finger songs first.
Don't bother with five finger melodies. Start by learning the entire major scale, how it sounds and common usage patterns for the scale degrees. After that proceed to work with the minor scales: natural, harmonic and melodic.
If you were to limit yourself to five finger melodies, you would not gain understanding of some important common use scenarios. For example: the relationship of the leading tone to the V chord, or melodies that use a plagal ambitus (e.g. Happy Birthday).