Who is the bringer of "liberty & civilization" in this cartoon & how is this person bringing these things?

I believe you are referring to Victor Gillam's "He Wouldn't Take It Any Other Way," published in the satirical magazine Judge in 1899. In this political cartoon, a Filipino, exaggeratedly caricatured as a savage and fearful man, partially dressed and in the wilderness, among ferns and cacti, has been cornered by a figure, only partially visible, presumably a U.S. soldier, on account of his attire and his firearm, who is the bringer of Liberty and Civilization on behalf on his country, as it is written in the paper that pierces his firearm and that he aims menacingly at the Filipino.

The bringer of "Liberty & Civilization" is, therefore, the United States, which, as the title of the cartoon ironically indicates, have tried to bring them peacefully and reasonably, but to no avail, hence the need to use intimidation, threat, and violence.

The cartoon is a criticism of U.S. Imperialism, which allegedly brought civilization and liberty to an already civilized nation, which was on the threshold of gaining its freedom and independence.      

the   square   deal   was   a   program   where   the   government gave any one   a fair   chance   to succeed

people can eat food during that time