The strike and disarm actions both have the attack trait, which means that they both suffer and increase the MAP, as described in the quote below.
The more attacks you make beyond your first in a single turn, the less accurate you become, represented by the multiple attack penalty. The second time you use an attack action during your turn, you take a –5 penalty to your attack roll. The third time you attack, and on any subsequent attacks, you take a –10 penalty to your attack roll. Every check that has the attack trait counts toward your multiple attack penalty, including Strikes, spell attack rolls, certain skill actions like Shove, and many others.
In this case, strike and disarm are subordinate actions of the disarming assault, but that doesn't alter their traits and effects, unless the disarming assault explicitly says so, as described in the following quote.
An action might allow you to use a simpler action—usually one of the Basic Actions on page 469—in a different circumstance or with different effects. This subordinate action still has its normal traits and effects, but is modified in any ways listed in the larger action. For example, an activity that tells you to Stride up to half your Speed alters the normal distance you can move in a Stride. The Stride would still have the move trait, would still trigger reactions that occur based on movement, and so on. The subordinate action doesn’t gain any of the traits of the larger action unless specified. The action that allows you to use a subordinate action doesn’t require you to spend more actions or reactions to do so; that cost is already factored in.
Hence, the answers to questions 1, 2, and 3 are all yes, because disarming assault doesn't modify how strike and disarm interact with the MAP.
Assuming it is the first action on your turn, the MAP after a disarming assault will be -5 or -10 depending on whether you used disarm: if you used both strike and disarm, the MAP afterwards will be -10; if you only used the strike, the MAP afterwards will be -5.
