Assalamalaykum.
Muslim too. Though I havent really been advertising it that much on Mumsnet as I am an occupational lurker. 
Boer with regards to your first question. I agree with HardlyEver. I think that you would probably still have to wear it as for many muslims the first reason for wearing hijab, is that it is a command from God in the same way that praying 5 times a day is or fasting in Ramadhan is or not eating pork is.
'There are certain rulings in Islam that can change according to place, time and situation. On the other hand we have rulings which are fixed and unchangeable. The only way a change would be possible is under dire circumstances like the threat of death, harm, sickness and other things.
The hijab is identified by all the scholars [except for a few non-Orthodox scholars over the last 20 years] as a fixed obligation which cannot change unless a qualified legal scholar deems that a sister?s situation demands it. Examples of this would be the Inquisition in Spain and the recent wars in Bosnia and Rwanda. However, it should be noted that such a change is, at least most of the time, considered temporal at best as it would fall under what are known as nawazil - temporary trials whose outcomes, for the most part, are not permanent'.
My personal understanding of the reason of why you have to wear hijab is that it is less about covering hair and more about identifying yourself as a muslim. One of the reasons the Quran gives for women covering is so that they are 'known' i.e. identifiable as Muslim. You can achieve the other goal of covering, which is modesty, without wearing a headscarf, but it is the headscarf which makes it clear to others that you are not just a woman who like to dress modestly but that you are also a muslim. This is important because first of all it impacts the way people (in particular men) interact with you and secondly it impacts the way you conduct yourself. As you are now identifiable as Muslim you unwittingly also become a representative of your faith. I know for myself this makes me much more cautious about how I behave when I am out and about (for example the way I speak to people) because I dont want any indiscretions to be linked or blamed on my faith. Kind of in the same way how a conscientious police officer or a soldier when they are wearing their uniform will behave in a way that dignifies their position as they do not want to bring shame on their profession. I hope that makes sense.
With regards to your second question I think it is inevitable that you will always get this oneupmanship not just about religion but with all things that you do that people could compete with you on. I typically have three responses to it I either find it annoying, amusing or just ignore it. Islamically speaking it is very frowned upon to boast about the religious acts that you do as sincerity is an incredibly important aspect of any 'good deed'. There is a very famous hadith which states that 'Actions are judged by their intentions'. So if your intention is to show off or to make others feel inferior then we believe that God does not accept your action as you did it for other reasons rather then as a means of drawing closer to God. An action that is very small for example doing something considerate for your neighbour, if done with sincerity can be more rewardable than a big action (like donating a lot of money to charity) if you are simply doing it to show off. I hope that makes sense.
If not I am sure there are others who can give a more coherent response than I can at this time of morning after being woken up three times during the night by my recalcitrant 3 month old ds.