  In this paper we present the results of our search for and study of $z
\gtrsim 6$ galaxy candidates behind the third Frontier Fields (FF) cluster,
MACSJ0717.5+3745, and its parallel field, combining data from Hubble and
Spitzer. We select 39 candidates using the Lyman Break technique, for which the
clear non-detection in optical make the extreme mid-$z$ interlopers hypothesis
unlikely. We also take benefit from $z \gtrsim 6$ samples selected using
previous Frontier Fields datasets of Abell 2744 and MACS0416 to improve the
constraints on the properties of very high-redshift objects. We compute the
redshift and the physical properties, such emission lines properties, star
formation rate, reddening, and stellar mass for all Frontier Fields objects
from their spectral energy distribution using templates including nebular
emission lines. We study the relationship between several physical properties
and confirm the trend already observed in previous surveys for evolution of
star formation rate with galaxy mass, and between the size and the UV
luminosity of our candidates. The analysis of the evolution of the UV
Luminosity Function with redshift seems more compatible with an evolution of
density. Moreover, no robust $z\ge$8.5 object is selected behind the cluster
field, and few $z$$\sim$9 candidates have been selected in the two previous
datasets from this legacy survey, suggesting a strong evolution in the number
density of galaxies between $z$$\sim$8 and 9. Thanks to the use of the lensing
cluster, we study the evolution of the star formation rate density produced by
galaxies with L$>$0.03L$^{\star}$, and confirm the strong decrease observed
between $z$$\sim$8 and 9.
