For 1) you are correct if there are no conditions on the executive or secretary being male/female (i.e. anything goes).
For 2) Consider the two choices separately (female president, male secretary) and remember that the choices are independent of each other (which means you can use the multiplication or product rule). Your answer is in-line with this (hopefully you can understand the answer based on what I've written).
For 3) You have to specify how they have been selected: you will get different answe rs based on how you select them (Q1 vs Q2)
For 4) What conditions does the treasurer have? (Are they male/female/both?)
For 5) List all of the possible combinations by hand - MMF MFM FMM and now add up the combinations
For 6) Probability = number of combinations for that event / total number of possibilities. You will need to answer 5 to get to 6.
Show us how you go with these hints and if/where you get stuck.