Can someone give a rundown of the halachos of conducting one's self in the bathroom ( including how much one can remove his clothing ? )
This is a good question. A good place to start would be to read the Kitzur Shulchan Aruch, Siman 4. If you have a Kleinman Edition Kitzur by ArtScroll, they have a brilliant linear translation method, and if you do not have a set you can purchase one here.
Siman 5 also provides loads of halachos about cleanliness, for further reading.
Here is a rundown of [some] of the halchos regarding composure and behavior in the bathroom. All of these halachos come from Siman 4 of the Kitzur Shulchan Aruch:
One should accustom himself to using the bathroom both in the evening and in the morning.
One should not hold back his bodily functions, as it transgresses the passuk "Do not make yourselves abominable." (Vayikra 20:25) Also, a man must not hold himself back from urinating because this transgresses the passuk "There shall be no sterile man among you." (Devarim 7:14)
A person must behave modestly in the bathroom by uncovering only what is necessary. A person has to be careful to do this in the night as well as the day.
One shouldn't relieve himself in front of any person, not even a idolater. But you can urinate in public if necessary, as to not hold yourself back from urinating, which is a transgression in itself (as explained before).
One shouldn't relieve himself while standing and shouldn't force himself to defecate by straining, because doing this might tear the muscles that hold the rectum.
One shouldn't hasten to rush from the bathroom until he's sure he is finished with his business.
When urinating while standing, a man must be careful to not drip urine on his shoes or clothing, and he shouldn't hold his organ with his hands.
One cannot contemplate Torah thoughts in the bathroom. Instead, one should think about business matters, so he doesn't start thinking about Torah or sinful thoughts, Chas ve'Shalom. When one cannot think about business (like on Shabbos), he should think about the things he's seen or heard that's interesting.
One should wipe himself well after defecating, because if there is anything left behind in his rectum he cannot recite sacred words.
One shouldn't wipe himself with the right hand, because he uses it to tie tefillin on his left arm. In the same way he shouldn't use the middle finger on his left hand because this is the finger he wraps tefillin onto.
Every time one uses the bathroom, even just a small amount, he should recite the Asher Yatzar blessing. If he forgets to recite this blessing, he should recite it when he remembers, once, not twice. One who took a laxative (a pill that cleans one's bowels out) shouldn't recite Asher Yatzar until he is sure the laxative has completed its job.
Hope this helps. There are additional laws, but please read the links I provided if you want to learn more.
Halachos of the Bathroom Written by Rabbi Moishe Dovid Lebovits of KOF-K Kosher Supervision gives a summary of the halachos of the bathroom. However, it does not deal with the subject of removing ones clothing. The article is too big to summarize here and I do not have the time to add the halachose regarding clothing right now.
Have a good Shabbos