Question

First order reaction does not depend on which factor

Answer 1

Independent of the unit in which concentration is expressed.

Answer 2

 are considering homogenous first order irreversible reaction

Half life is given by : ln2/k
K is the rate constant. Which depends upon temperature, ionic strength, suface area of reactant, light irradiation,presence of catalyst .

The k term is included in the rate law  to denote the temperature dependency of the rate of reaction. 
 K = k. e^-E/RT
E denotes the activation energy 
R denotes the gas constant
K. Is the frequency factor( total collision between reacting molecule per second)
T is the temperature

So K ( rate constant )depends on temperature and not on concentration.And hence the half life for first order homogeneous irreversible reaction does not depend upon the concentration