My solution to **first** problem is 
>! $98$

This is the strategy:
>! First, everyone sends a mail to $A$ ($49$ mails in total). Then $A$ sends a mail to everyone else ($49$ more mails).  
>! Why is this optimal? To share his information, everyone must send at least an email, though if they want to know other information, they must receive at least a mail as well! So, $49+49=98$ is necessarily the minimum!

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My solution to the **second** problem is
>! $96$ 

The strategy is:
>! Choose $4$ people in the group $(A,B,C,D)$. The other people send an email to one of these, doesn't matter who. This is $50-4$ mails. Those $4$ people then share their knowledge between themselves, so that they know everything. This process requires only 4 mails. Then, they send back an email to the "ignorants", which takes again $50-4$ mails.