1) What does Islam say about keeping pictures of those who have left us?
As a form of remembering them, reminiscing on good memories, etc.
2) What does Islam say about taking pictures of someone who has passed.
For example, if someone has passed away in another country and the family can’t go to attend the funeral, is it permissible to take pictures of the person who has passed away and/ or the funeral to share with ONLY the family of the deceased?
3) Do the answers for the above questions vary for men and women?
1) it's a matter of taqwa...in STRICT Islamic terms...taking pictures of living beings or keeping them is recommended...it's NOT like if you take pictures or keep them, you have committed gunaah-e-kabeera...it's NOT like that...it's a matter of taqwa as i said in my opening sentence. the more the taqwa the greater the incentive to refrain from makrooHaat. same is true with music and other laho la'b.
the ultimate goal of a Muslim is to be muttaqii and it comes gradually. let your inner self make a judgement call to acquire taqwa in steps...that way, it will be genuine and long lasting. i mean when your innerself is ready to forge ahead with taqwa. that will be a real thing, not just a trial.
as an average Muslim, i would worry more about the basics in the begenning and then i'll let taqwa get a hold on me slowly and steadily. taqwa ba-tadreej is an ideal thing.
2) i think taking pictures of a dead person is not a good idea from either religious and non religious perspective.
since you do NOT have the dead person's permission/consent to take pictures, you should refrain from doing so. it's only fair and decent thing to do.
3) no, there is no difference when it comes to the sex of the picture taker.
Is taking picture of livings are permissible or not. Scholars have different views on that. Some say yes it is allowed but some other says no its haraam.
First of all one must know whether its permissible or not than come to next questions as u asked.
The argument for photographs falls in to matters of new things that were not present in the past ... As a result some people have classified photos as pictures and others have not ... Those who have not taken this stance have argued that there is no creativity in photographs, nor is there any form of idol worship, as images of livings things were only considered evil, because in the past they represented idols ... Today this is not the case. The balanced opinions suggest that keeping photos to a minimum is best, tucked away in albums and not on display to venerate the dead or living members in a way that resembles idol worship.
I was thinking something else. We know that there are many hadiths where drawing picture is forbidden and also disliked if there is pic in a home. So talking about the present, I would say that they studied and really studied hard to bring all those things/act in a Muslim which were prohibited/forbidden either by the order of Almighty Allah through Holy Quran or by sayings of our Prophet Muhammad