Woman Calling the Adhan and Iqamah

Assalamu alaikumAs a new Muslim, the day before Ramadan this year alhamdulillah, I strive to practice my deen as perfectly as possible however sometimes there is still confusion over some issues.  I therefore have two questions that despite asking on other boards/forums I cannot achieve a satisfactory answer.i)  Does a woman have to do the Adhan or Iqaamat in whatever case.  I have been told as a woman I do not have to, but recently when praying with another woman she asked if I was going to do the Iqaamat...ii)  I work full-time and pray three times during the course of my working day.  Is it permissable to run my hands over my hijab when making wudu, or do I have to take the hijab off for the wudu to be accepted?  I'm conscious of the time it takes me to make wudu and then pray during my working hours when my company has been very supportive of my conversion.  I have had differing answers with regard to this, some say yes, some say no, some say that it is permissable due to circumstances to wipe over socks and then do regular complete wudu when we get home, so if this is permissable then could this be applied to the hijab?iii)  Finally, this will be my first year as a Muslimah, alhamdulillah and Christmas is approaching.  The only family I have remaining is my father and although he is not religious, (we) do exchange gifts and cards.  How should I approach this, is it permissable to continue to exchange items? He is also very supportive, alhamdulillah, of my conversion however it will be 'strange' not to present him with gifts.  I am fully aware, alhamdulillah, of the psychology surrounding my feelings and know that I can give him gifts any time of the year, and actually Eid would be nice, it's just getting used to losing the tradition.  (My family are not religious in general.)Alhamdulillah my concern is obviously to do what is correct and that is why I am seeking the truth, insha'Allah.JazakAllah khayran for the advice you are able to give.Assalamu alaikum