Sample data

    structure(list(Gene = c("A", "A", "A", "A", "B", "C", "C", "D", "D", "D"), Peptide = c("a1", "a2", "a3", "a4", "b1", "c1", "c2", "d1", "d2", "d3"), Sample1 = c(0.275755732, 0.683048798, 1.244604878, 0.850270313, 0.492175199, 0.269651338, 0.393004954, 0.157966662, 1.681672581, 0.298308801), Sample2 = c(0.408992244, 0.172488244, 1.749247694, 0.358172308, 0.142129982, 0.158636283, 0.243500648, 0.095019037, 0.667928805, 0.572162278), Sample3 = c(0.112265765, 0.377174168, 2.430040623, 0.497873323, 0.141136584, 0.250330266, 0.249783164, 0.107188279, 0.173623439, 0.242298602), Sample4 = c(0.87688073, 0.841826338, 0.831376575, 0.985900966, 0.891632525, 1.016533723, 0.292048735, 0.776351689, 0.800070173, 1.161882923), Sample5 = c(1.034093889, 0.304305772, 0.616445765, 1.000820463, 1.03124071, 0.995897846, 0.289542364, 0.578721727, 0.672592766, 1.168944588), Sample6 = c(1.063124715, 0.623917522, 0.613196611, 0.990921045, 1.014340981, 0.965631141, 0.316793011, 1.02220535, 1.182063616, 1.41196421), Sample7 = c(1.335677026, 0.628621656, 0.411171453, 1.050563412, 1.290233552, 1.1603839, 0.445372411, 1.077192698, 0.726669337, 1.09453338), Sample8 = c(1.139360562, 0.404024829, 0.263714711, 0.899959209, 1.356913804, 1.246338203, 0.426568548, 1.104988267, 0.964924824, 1.083654341), Sample9 = c(1.38146599, 0.582817437, 0.783698738, 1.118948066, 1.010795866, 1.277086848, 0.434025911, 1.238871048, 1.201184368, 1.476478831), Sample10 = c(1.111486801, 0.60513273, 0.460680037, 1.385702246, 1.448873253, 1.364329784, 0.375032044, 1.382750002, 0.741842319, 1.035657705)), row.names = c(NA, -10L), class = c("tbl_df", "tbl", "data.frame"), spec = structure(list( cols = list(Gene = structure(list(), class = c("collector_character", "collector")), Peptide = structure(list(), class = c("collector_character", "collector")), Sample1 = structure(list(), class = c("collector_double", "collector")), Sample2 = structure(list(), class = c("collector_double", "collector")), Sample3 = structure(list(), class = c("collector_double", "collector")), Sample4 = structure(list(), class = c("collector_double", "collector")), Sample5 = structure(list(), class = c("collector_double", "collector")), Sample6 = structure(list(), class = c("collector_double", "collector")), Sample7 = structure(list(), class = c("collector_double", "collector")), Sample8 = structure(list(), class = c("collector_double", "collector")), Sample9 = structure(list(), class = c("collector_double", "collector")), Sample10 = structure(list(), class = c("collector_double", "collector"))), default = structure(list(), class = c("collector_guess", "collector"))), class = "col_spec"))

Scripts

     df %>% gather(k,v, -Gene, -Peptide) %>% split(.$Gene) %>% map(~spread(.,Peptide, v)) %>% map(~select(.,-1:-2)%>% ggpairs(.))


Q1.  How can I add protein name to the plots and save these plots separately in a folder?

Q2. How can put peptide comparisons (for each proteins) faceted and save?
@OP: Q1 and Q2:

For Q1 requirement: try this with  code 

    p=df1 %>% gather(k,v, -Gene, -Peptide) %>% split(.$Gene) %>% map(~spread(.,Peptide, v)) %>% map(~select(.,1:ncol(.))%>%ggpairs(3:ncol(.), title = paste0("Protein: ",unique(.[,1]))))

for png (This would create 4 png files with gene/protein names as file name and each file will have the string "protein" and protein name in the data frame .. Change resolution as per  requirement.):

    for(i in 1:length(p)){
    ggsave(plot = p[[i]], file = paste0(names(p)[i],".png"), dpi = 300)
    }

For Q2: There is manual way, you can automate it.

    library(cowplot)
    plot_grid(
        ggmatrix_gtable(p[[1]]),
        ggmatrix_gtable(p[[2]]),
        ggmatrix_gtable(p[[3]]),
        ggmatrix_gtable(p[[4]]),
        nrow = 2,
        ncol=2
    )


<a href="https://ibb.co/nrx5cJ"><img src="https://preview.ibb.co/bv5DWd/Rplot.png" alt="Rplot" border="0"></a>