Hello is there a problem with the tzitzis of a Talis Gadol touching or dragging on the floor ? Is one allowed lchatchila to hold all the tzitzis in his hand the whole davening to prevent the tzitzis from dragging on the floor from movement in the middle of tfela ? Is it better to have the whole upper body(including the arms) wrapped in the tallis or wrap it like most people do , which the arms are not wrapped in the Talis?
Yes, one should be careful to refrain from allowing the tzitzis strings from touching the floor.
This matter has actually been broadly discussed by Poskim, and some are lenient for certain circumstances – but the general consensus is that one should refrain from this.
You can wrap the tallis as you think best, provided it wraps around the upper body.
The first source for this matter is the Baalei HaTosafos on Parashas Eikev, who writes that one should not drag tzitzis on the floor. This is echoed by the Agur and the Rokeach.
The Shaarei Knesses HaGedolah asks from the Gemara in Berachos where we find that one should not have one’s tzitzis dragging on graves because of lo’eg larash. He answers that 1) we can suggest that the tzitzis were not dragging on the ground but only on graves, and 2) we can suggest that there is only a degradation of the tzitzis when a person is walking, and not when a person is in one place.
The Magen Avraham (21) asks further questions, and according to one of his answers, one must only be careful when putting on the tallis, but when waking with the tallis there is no problem.
For more details see Rav Tzi Cohen’s Sefer HaTzitzis, who notes that from the Graz it emerges that there is always a problem of dragging tzitzis, and the general language of other acharonim indicates that one should always refrain from this.