I have three d20 dice with the following number arrangements:
Each pair of opposite sides add up to 21. 1 shares edges with (clockwise) 2, 5, and 8, and shares vertices with (clockwise) 2, 3, 4, 5, 6, 7, 8, 9, and 10. 10 shares edges with (clockwise) 2, 9, and 15, and shares vertices with (clockwise) 2, 1, 8, 9, 17, 16, 15, 14, and 3.
Each pair of opposite sides add up to 21. 1 shares edges with (clockwise) 13, 7, and 19, and shares vertices with (clockwise) 13, 5, 15, 7, 17, 3, 19, 6, and 11. 10 shares edges with (clockwise) 8, 17, and 12, and shares vertices with (clockwise) 8, 16, 3, 17, 7, 15, 12, 2, and 20.
The pairs of opposite sides are 1 & 20, 2 & 12, 3 & 17, 4 & 16, 5 & 19, 6 & 14, 7 & 13, 8 & 18, 9 & 15, and 10 & 11. 1 shares edges with (clockwise) 13, 10, and 6, and shares vertices with (clockwise) 13, 12, 17, 10, 4, 8, 6, 9, and 19. 10 shares edges with (clockwise) 17, 4, and 1, and shares vertices with (clockwise) 17, 15, 5, 4, 8, 6, 1, 13, and 12.
Do the different arrangements affect any aspects of the probability for rolling each value for each die?
No, the arrangements have no bearing on the probability (assuming the effect of paint or grooves from the number markings are negligible). As long as the dice are symmetrical, all 20 sides have equal probability of being rolled.