I am trying to compose a fuga for two voices. What I want to ask is, is it a requirement to be the same for the countersubjects that come after subject in exposition part? I mean, are the firstly introduced countersubjects in each voice, expected to be same or may I use another countersubject instead of transposing the first to dominant pitch? And do you have any little trick to put some Bach flavour into my fugue? It is said that Bach used neighbour tones in circle of fifths, such as that.
If you are writing a fugue in the Baroque style (sidenote, the fugue was already out-dated by Bach's day), then the subject-answer relationship is almost invariably tonic-dominant (hence the terms 'subject' and 'answer') - even in Shostakovich's 48. Regarding the counter-subjects: they are frequently varied. Download a copy of the WTC from imslp and have a look. The fugue is one of the least severe contrapuntal forms/techniques (compare with the canon). No two fugues of Bach's are the same in structure. There is no model - we invented it. In my lectures, I teach the "form" through comparative analysis. If you want to imitate Bach, look at the melodic/rhythmic character; tonic-dominant (or cycle of 5ths) was not at all unique to Bach. Happy composing!
If you are playing different ideas against each subject entry, they are not countersubjects, They are free voices. There is nothing wrong with doing it that way - it is, in fact, more common than using countersubjects (pre-Bach, it is the norm). Countersubjects, if used, can be varied between different groups of entries (or remain the same). There is considerable freedom available in this regard.
In two-part writing, however, you may find that a consistent countersubject is useful for lampshading the subject entries. The two voices in two-part writing can be a bit busy doing the work of four, so subject entries can be hard to highlight in the "chatter" at times.
Bach-like counterpoint? Watch your rhythm. You don't want the voices always in lockstep. Try to ensure that the two voices have different rhythmic patterns that fit together well. Passages where they use the same rhythm should serve as contrast, not the norm.
Bachian "tricks"; (1) Ensure that the rhythm of the piece matches the shortest note value. That is, if a quaver is your shortest not, make sure that on every 8th part of every bar that a new note plays. Do not, for example, have all voices play whole notes for a bar, but fill all the "gaps". If one voice is resting on a longer note, fill in the "gap" by making another voice active. Think of a metronome ticking to the time of your shortest note value, and make sure that one new note starts on every metronome tick. (2) When one voice takes a rest on a note, have another voice imitate the voice of the voice that is resting - like a conversation: when one person stops talking, another starts talking.
No, it isn't necessary to retain the same counterpoint throughout the fugue. There are many more fuges varying the accompanying voices than reusing them strictly.
On the other hand, if you do keep it around, that would be a very Bach thing to do. Many of his larger fugues, particularly in vocal works, are permutation fugues, where essentially all voices from the exposition are kept around and rearranged.
(On the third hand, two-piece writing is very much unlike Bach in the first place, so emulating a double fugue probably isn't the most natural way to pay homage!)