Have a look at the "Tips and notes" of this lesson. For stative verbs, the casual form of the verb is used to form this structure.
Now... to stand and to sit being stative verbs in Korean, that is a bit strange to me. But I guess we just have to accept these things.
The verbs might be more closely connected to "to be sitting" and "to be standing" then. Not sure...
not really....it's saying she is thinking and is used as an adjective because of the -하는 so it needs to go before woman. if it went after it makes it sound like she is doing two verbs and while technically correct it needs to be said as an adjective like it is in the sentence.