What are the signs of Allah's love for His slave?

 As-salamu `alaykum. I work in a software company where the dress code is business formal. So, it’s compulsory to wear shoes. The thing is I have to remove my socks and shoes every time I make wudu’. I heard that it’s not necessary to remove socks for wudu’. Well, I'm not sure about that and its procedure. So, if there is any alternative to this, then, please, enlightenment me on this. Jazaka Allah khair.

We celebrate the birthday of Prophet Muhammad (peace be upon him). On this day, we read a lot of salutations on him and engage in a lot of prayers to Allah. We try to show our love for our Prophet (peace be upon him). How come you say we cannot do it?
 

I would like to know the proper way to make du’aa’ during prayer, as the Prophet (peace and blessings of Allaah be upon him) did it. Is it after the prayer or between the two prostrations or whilst standing or when?.

Some mobile phones have a Quraan programs which enable one to read the Quraan anytime on the mobile’s screen. Is Taharah (Purity) a condition before one starts reciting?.

Is it permissible to pray in a mosque where the ground floor is controlled by the Shi‘ah and the Sunnis control the upper floor?

I have a few questions concerning parents:
1. What right does my Mother have over me? 
2. What right do I have over my mother? 
3. What do I have the freedom to do (which is Halal or Mubah, Ofcourse) without my Mother having the right to stop me? 
4. When does the Father have the final say in a matter? 

I love my mother very very very much. She is very over protective, and sometimes I feel like I'm in chains. I know she is doing it out of extreme love for me. How can I tell her that I need a little choice of my own in life.

What is the definition of gheebah and what is the ruling on it?

I want to make my children keen to pray, because they will pray once then forget about prayer many times. I always advise them and pray to Allah to guide them. How can I encourage them and make them love prayer?.

My neighbour is an American Christian, and she and her family brought me a gift when it was Christmas. I could not refuse the gift, lest she be offended.  
Can I accept this gift, as the Messenger (peace and blessings of Allaah be upon him) accepted gifts from kaafirs?

I don't celebrate Christmas in any way, but my 11 year old daughter loves the beauty of a Christmas tree when decorated. Is it permissible for me to have one in my house throughout the year?

I understand that hijab is required, and I’ve been wearing it for some time now but I feel like putting it on might have been a mistake.  I don’t feel like it’s made me become a better Muslim, and I feel almost like I’m deceiving people because they look at me as an example even though I’m still struggling with a lot of things. Also, if I take it off, is it really something Allah will punish me for? It seems like such a petty thing. Isn’t the most important thing having a clean heart?