Solution:

Empty.

(mpt, emty or mt depending on your interpretation)

Solution:

5795
+ 6435
+ 2505
------
14735

5305
+ 2475
+ 6595
------
14375

Solution:

14

Explanation
If the beggar can make a whole cigarette from 6 butts then he can make 12 cigarettes from the 72 he found. Once he smokes those, he then will have another 12 butts, which gives him enough to make another 2 cigarettes. A total of 14.

Solution:

BACK

All the others can also be read backwards as proper words.

Solution:

61

Reversed digits of squares of number in descending order.

Solution:

Submarine

Solution:

Each word has 3 consecutive letters of the alphabet-
couGHIng (GHI)
thiRSTy (RST)
DEFiant (DEF)

Solution:

129.

These are the first 10 prime numbers (2, 3, 5...) prefixed with a 1

Solution:

SQRT(.2 ^ -2)

Take .2 and raise it to the power of -2 and then take the square root.

Solution:

HighJacking (High+Jack+King)