I am a beginner in violin. I am confused that most of the times in music sheet the notes are normal (neither sharp or flat) but when playing it feels like one is playing the sharp of some notes (like F# instead of F, and the second finger positions). Is that the right way?
One of the important things to consider when learrning violin is learning to listen to the exact pitch of any notes played. Seems like you're doing that, so good. Also, it seems you're pressing the strings down in not the exact right place. If the notes sound sharp, it's because your fingers are moving too far along the neck, chinwards. So, move them back until the notes sound right in tune.
It's a common beginner problem, maybe caused by the way you're holding the violin. The left hand should not be supporting the neck, its job is fingering the notes.
When you start playing the violin the first finger pattern you usually learn is a pattern where there is:
a whole step (a major second) from open string to the first finger,
a whole step from first finger to second finger,
a half step (a minor second) from second finger to third finger,
and if you include the fourth finger a whole step from third to fourth finger.
With that pattern on each string the "normal" notes on the violin for a beginner is as follows:
On E-string: E - F♯ - G♯ - A - (B)
On A-string: A - B - C♯ - D - (E)
On D-string: D - E - F♯ - G - (A)
On G-string: G - A - B - C - (D)
The note in the bracket is the fourth finger which is the same note as an open string except the B on the E string.
With that finger pattern you can play:
an A major scale in one octave on the A and E strings and play tunes in A major on those two strings.
a D major scale in one octave on the D and A strings and play tunes in D major on those two strings.
a G major scale in one octave on the G and D strings and play tunes in G major on those two strings.
That is the most common finger pattern for beginner violinists. It is the best way to start. You have the open strings as reference for intonation; the root note of the scale, the tonic, is an open string and the dominant is an open string. It helps a lot in order to develop your sense of intonation.
Do NOT start with C major. It is much harder to play C major in tune for a beginner especially on the E string.
Thus the "normal" notes on the violin do include sharps.
I think you might be running into the issue of key signatures. When you look at the very beginning of a piece, you see a clef and then (usually) you see some sharp or flat symbols, and then you see a time signature (3/4, C, or something like that). The sharps and flats are automatically applied to all the notes. So if you see an F# (just the sharp, no note) before the time signature, any time you see an F in the piece, it's actually an F#. There's a good description of how key signatures work here.
If that's not what you're looking for, you might be having issues with intonation. When you play a G on the E string, try playing open G and then the high one and comparing them. They're both Gs, so they should sound like the same note. If you're playing another second finger note, you can test it against another source. There are various apps you can use, or you can search the web.
NOTE: if you're going to compare your note to one from another source, MAKE SURE YOUR INSTRUMENT IS IN TUNE!! If your violin isn't in tune, you'll be training your fingers to go to the wrong places.