を marks the direct object of the verb.
Here, the verb is まくる = to roll up, and the thing being rolled up is 袖.
So:
Here まくる means to roll up or to fold back, especially for things like:
So シャツの袖をまくる means to roll up your shirt sleeves.
This is a very natural verb for clothing in this context.
Yes, but the nuance changes a little.
In this sentence, と works well because it presents the idea as a general truth: rolling up your sleeves makes washing easier.
洗い物 literally means things to wash or washing-up.
In everyday context, it often means:
Depending on context, it can sometimes refer more broadly to things being washed, but here it most naturally means doing the dishes.
Because しやすい means easy to do, and the thing being described as easy takes が.
So:
Think of しやすい as describing the activity.
Also, 洗い物 is a verbal noun here, and する is understood:
Using を directly before しやすい would sound wrong here.
It comes from:
So:
This pattern is very common:
Japanese often omits the subject when it is obvious or unimportant.
This sentence is making a general statement, something like:
The subject is understood generically as you, one, or people in general. Adding 私は would make it more specifically about me.