I recommend using POSIX format when you want to work with time series and ggplot2.
Note that you have to handle to week 00, which are the first days of January ending the 52th week of December.
## Fake data / without a reproducible example
set.seed(1)
df = data.frame(year = c(rep(2015,14), rep(2016,21)),
month = c(rep(12,14), rep(01,21)), day = c(seq(18,31,1), seq(01,21,1)),
create = sample(c(1,2,3,NA),35, replace = T, prob = c(0.3,0.3,0.3,0.1)),
verified = sample(c(1,2,3,NA),35, replace = T, prob = c(0.1,0.1,0.1,0.7)),
trans = sample(c(1,2,3,NA),35, replace = T, prob = c(0.1,0.2,0.1,0.6)))
# Add of week information
df$date_posix = as.POSIXct(paste0(df$year, "-", df$month, "-", df$day))
df$week = strftime(df$date_posix ,format = "%W")
# summarize
require(plyr)
#> Le chargement a nécessité le package : plyr
df_sum = ddply(df, "week", summarize,
create_sum = sum(create, na.rm = T),
verified_sum = sum(verified, na.rm = T),
trans_sum = sum(trans, na.rm = T))
# melt
require(reshape2)
#> Le chargement a nécessité le package : reshape2
df_sum_melt = melt(df_sum, id = "week")
# plot
require(ggplot2)
#> Le chargement a nécessité le package : ggplot2
ggplot(df_sum_melt, aes(x = week, y = value, fill = variable)) +
geom_bar(stat = "identity", position = "dodge")

Created on 2018-09-18 by the reprex package (v0.2.0).
EDIT (the tidyverse way)
library(tidyverse)
library(lubridate)
#>
#> Attachement du package : 'lubridate'
#> The following object is masked from 'package:base':
#>
#> date
set.seed(1)
tibble(year = c(rep(2015,14), rep(2016,21)),
month = c(rep(12,14), rep(01,21)), day = c(seq(18,31,1), seq(01,21,1)),
create = sample(c(1,2,3,NA),35, replace = T, prob = c(0.3,0.3,0.3,0.1)),
verified = sample(c(1,2,3,NA),35, replace = T, prob = c(0.1,0.1,0.1,0.7)),
trans = sample(c(1,2,3,NA),35, replace = T, prob = c(0.1,0.2,0.1,0.6))) %>%
mutate(date_posix = as.Date(paste0(year, "-", month, "-", day)),
week = lubridate::week(date_posix)) %>%
group_by(week) %>%
summarise(create_sum = sum(create, na.rm = T),
verified_sum = sum(verified, na.rm = T),
trans_sum = sum(trans, na.rm = T)) %>%
gather(variable, value, -week) %>%
ggplot(., aes(x = factor(week), y = value, fill = variable)) +
geom_bar(stat = "identity", position = "dodge")

Created on 2018-09-18 by the reprex package (v0.2.0).