Open a Door: MEA (PH p. 128, Table 8-4).
Climb 1/4-Speed: MEA (PH p. 128, Table 8-4);
Steep Slope: Move x1/2 (PH p. 143, Table 9-4).
Absolutely no restrictions on moving through friendly spaces (PH p. 130).
Using the same logic of Take 20 taking twenty times as long, Take 10 might take 2 rounds - one in every twenty rolls of a d20 is a 20, one in every two rolls of a d20 is above 10.
But since it's just considered an "average" roll, it only takes one round.