Displaying percentages within category for continuous/ordered variable (with ggplot)

I have two questions, the first a (hopefully) straightforward mechanical one and the second more theoretical (though still with a technical element).

1. I am trying to do something nearly identical to this question, but I have a variable that is ordered/continuous (0 - 4), instead of a 1/0 dichotomous variable, which means that filtering == 1 will not work. To summarize here, I simply want to display the percent of each level within each race category.

2. I am also hoping to figure out a way to display those descriptive results for all 3 questions in just one figure. I first thought about trying to do some type of facet_wrap() with each variable (question1, question2, question3) being its own panel. Would that require pivot_longer() to make my data long instead of wide? Another thought was to have just one figure/panel, but each x axis tick is a race category instead of a question, and then it'd have 3 bars for each of the 3 questions. I'm not sure how I'd get that to work, though.

Thanks in advance and sorry for this wordy question. Here is some example data:

set.seed(123)

d <- data.frame(
  race = sample(c("White", "Hispanic", "Black", "Other"), 100, replace = TRUE),
  question1 = sample(0:4, 100, replace = TRUE),
  question2 = sample(0:4, 100, replace = TRUE),
  question3 = sample(0:4, 100, replace = TRUE)
)

How about this:

  library(tidyverse)
set.seed(123)
d <- data.frame(
  race = sample(c("White", "Hispanic", "Black", "Other"), 100, replace = TRUE),
  question1 = sample(0:4, 100, replace = TRUE),
  question2 = sample(0:4, 100, replace = TRUE),
  question3 = sample(0:4, 100, replace = TRUE)
)

d %>%
  pivot_longer(-race, names_to = "question", values_to = "vals") %>% 
  group_by(question, race, vals) %>% 
  tally() %>% 
  group_by(question, race) %>% 
  mutate(pct = n/sum(n)) %>% 
  ggplot(aes(x=race, y=pct, fill=as.factor(vals))) + 
  geom_bar(position="stack", stat="identity") + 
  facet_wrap(~question) + 
  scale_y_continuous(labels = scales:::percent) + 
  labs(x="", y="Percentage (within Race)", fill="Response") + 
  theme_bw() + 
  theme(legend.position = "top", 
        panel.grid = element_blank(), 
        axis.text.x = element_text(angle = 45, hjust=1))

^{Created on 2022-05-23 by the reprex package (v2.0.1)}