Do we hold that one shouldn’t take a piece off the bread with one hand and eat with the other hand?

The rule of not holding the food in one hand and tearing off a piece with the other hand applies only to food which is on a plate. Food which is normally held by hand such as bread may be eaten that way.

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דברי חמודות חולין ח, צד. הגהות מהר״א אזולאי ללבוש קע, ה. א״ר שם יא. שמן המאור שם ט.