Disinformation is listed as one of the extended actions as part of Ship Combat. The rule book explicitly states that the modifiers for extended actions may be modified at the GM's discretion. (pg 215 Core Rulebook)
The Disinformation action can be taken once per strategic round by a character that has not participated in any other action that round(which is supposed to represent approx. 30 mins of in-game time).
The rules do not explicitly say you cannot perform this action over multiple rounds, but again it falls down to the GM to decide if is appropriate.
For example, say your ship is surrounded by a fleet of chaos worshiping cultists who are determined to invade the ship and cannibalize the entire crew. You definitely don't want to worry your crew with that information, so you can use the disinformation skill to downplay the threat being faced or what not. Now, say you keep downplaying the threat, turn after turn...won't some of the smarter crew members start getting a bit suspicious? Your GM may decide to ramp up the difficulty on each of the following Disinformation actions .
As I mentioned, this is down to the GM's discretion regarding allowing you to perform this test over multiple rounds. RAW allow you to do that and to stack the bonus and also allow the GM to modify the difficulty of such actions
For the second question, there is nothing in the rules that states you can 'pick and choose' which result to apply.