Concerning the fingering in measures 1-4 of BWV 556, if you play it with the usual technique, it feels strange to your hand. However, if you use them correctly like I will teach you now, they will be perfectly natural and most importantly, they will create the articulate legato touch for you without you having to think about them.
You see, the fingering in this piece is based on the paired fingering technique meaning the strong fingers are placed on the stronger beats. Although in measure 1 you could say, 3434 looks like finger crossing, it is in fact, finger shifting. This means you should not attempt to play legato and cross over 3 after 4. Instead, play 34 and shift the entire hand to the new position for another 34. In other words, move your fingers together as a unit. When you shift this way, you are naturally articulating correctly.
In measure 3, the right hand part has pairs of thirds which look like this: 2/4 1/3 2/4 1/3. Do not try to cross your fingers but shift your hand from 1/3 to 2/4. Crossing would be very inconvenient but shifting will naturally create a break between the pair of thirds.
The same thing applies to the pedaling in the fugue. Try to move both of your feet together as a unit on eighth and sixteenth notes.
Another important principle to notice is the finger skipping technique. This means that the same intervals (especially wider ones) should be played with the same fingers. For example, in measure 4 from end of the fugue you can see the 4 consecutive sixths in the right hand part which could be played with 1/5 1/5 1/5 and 1/5 fingering.
Be careful not to make very large breaks between the notes also which make the music sound choppy and unconnected. The touch should be singable or as Bach calls it "cantabile manner of playing".
When you are good in articulating this way, you could also make subtle adjustments in order to emphasize the meter. Make larger breaks between the stronger beats.
As far as accuracy in triplets of the prelude are concerned, try not to lift your fingers off the keyboard and stay in contact with the keys at all times. This will help you to improve your accuracy.
For best results, practice in separate voices, 2 voice combinations, 3 voice combinations and only then the entire 4 part texture. Do not play the entire piece from the beginning until the end (at least at first). Instead, choose a fragment of about 4 measures and master each combination in it. Then take another fragment and so on. After you learn all the fragments, combine them together, playing 1 line, 2 lines, 4 lines, 8 lines, 16 lines and so on without stopping.
Bottom line: the early fingering helps to achieve the desired articulation. Do not reach for the keys but instead shift the entire hand or both feet into a new position. Make it as connected as possible but not legato.
By the way, if you need complete fingering and pedaling of Prelude and Fugue in F Major, BWV 556, check out my practice score.
When you click on this link you will be able to see the preview of the actual score with fingering and pedaling which helps to create ideal articulation (articulate legato) naturally.
Or do you want to learn my special powerful techniques which help me to master any piece of organ music up to 10 times faster? If so, download my FREE Organ Practice Guide: http://www.organduo.lt/organ-tutorial.html