What type of illness that permits breaking the fast in Ramadan?
It is an illness that, if one fasts, there is a fear it may lead to their death or cause unbearable hardship.
Which is better for a traveler: fasting or breaking the fast?
Fasting is better, unless it causes hardship—in that case, breaking the fast is better.
Is Zakah (obligatory charity) due on leased property, and how is it calculated?
Zakah isn`t due on the leased property itself, but on the saved income from that property if it reached Nissab (minimum amount liable for Zakah), and a whole lunar year had lapsed over saving it.
Can someone who begins a voluntary fast break it?
It is preferable for someone who begins an act of worship not to break it.
Allah the Exalted has said {what means}: "and let not your [good] deeds come to nought!" [Muhammad/33].
However, if a person starts a voluntary fast (nafl) and needs to break it, they are going against what is preferable, but there is no sin upon them.