A subset of some set X is, by definition, any set whose elements are entirely contained in X. So the answer is yes. As an example, take your infinite set, and select 3 or 10 or any finite number of...
YES
They are numbers that terminate.
An empty set is considered a finite set because it contains zero (0) elements and zero is a finite number.
The empty set is a subset of all sets. No other sets have this property.