For the first question: In DESeq2 I think you need to use a list with the contrast argument in results() to test fold changes of fold changes. I usually do this in limma so others might correct me if this is not accurate.

Here is a toy example:

library(DESeq2)

# Intercept-less (~0) design to make all groups accessible as coefficients in resultsNames()
set.seed(1)
dds <- makeExampleDESeqDataSet(n = 5000, m = 20, )
dds$group <- factor(rep(LETTERS[1:4], each = 5))
design(dds) <- ~ 0 + group
dds <- DESeq(dds)
res <- results(dds, contrast = list(c("groupA", "groupB"), c("groupC", "groupD")))

# Plot the one with smallest pvalue
gene_to_plot <- rownames(res[which(res$pvalue == min(res$pvalue, na.rm = TRUE)),])

data <- plotCounts(dds = dds, gene = gene_to_plot, intgroup = "group", returnData = TRUE)

library(tidyverse)
library(ggpubr)
data %>% mutate(membership = if_else(group %in% c("A", "B"), "ONE", "TWO")) %>%
  ggplot(aes(x = group, y = count, color = membership)) +
  geom_point(position = position_jitter(.2, 0, 0), size = 3) +
  stat_summary(fun = mean, geom = "crossbar", size = 1)

Here is a plot assuming A and B are treatment and control of cell line 1 and C and D of cell line 2.

For the second question, if you have the same control then you can directly compare the groups, like A-B, B-C, A-C. Does this make sense?