diff --git a/r/R/dplyr-functions.R b/r/R/dplyr-functions.R
index a1fa715646d..b35c87e87f3 100644
--- a/r/R/dplyr-functions.R
+++ b/r/R/dplyr-functions.R
@@ -825,3 +825,10 @@ agg_funcs$var <- function(x, na.rm = FALSE, ddof = 1) {
     options = list(ddof = ddof)
   )
 }
+agg_funcs$n <- function() {
+  list(
+    fun = "sum",
+    data = Expression$scalar(1L),
+    options = list()
+  )
+}
diff --git a/r/src/compute.cpp b/r/src/compute.cpp
index aec9d9a9f50..5468fa83113 100644
--- a/r/src/compute.cpp
+++ b/r/src/compute.cpp
@@ -177,8 +177,12 @@ std::shared_ptr<arrow::compute::FunctionOptions> make_compute_options(
       func_name == "hash_all") {
     using Options = arrow::compute::ScalarAggregateOptions;
     auto out = std::make_shared<Options>(Options::Defaults());
-    out->min_count = cpp11::as_cpp<int>(options["na.min_count"]);
-    out->skip_nulls = cpp11::as_cpp<bool>(options["na.rm"]);
+    if (!Rf_isNull(options["na.min_count"])) {
+      out->min_count = cpp11::as_cpp<int>(options["na.min_count"]);
+    }
+    if (!Rf_isNull(options["na.rm"])) {
+      out->skip_nulls = cpp11::as_cpp<bool>(options["na.rm"]);
+    }
     return out;
   }
 
diff --git a/r/tests/testthat/test-dplyr-aggregate.R b/r/tests/testthat/test-dplyr-aggregate.R
index 7c2f7f890b9..8d68bbaf48e 100644
--- a/r/tests/testthat/test-dplyr-aggregate.R
+++ b/r/tests/testthat/test-dplyr-aggregate.R
@@ -154,10 +154,26 @@ test_that("Group by var on dataset", {
   )
 })
 
-
-test_that("Group by any/all", {
+test_that("n()", {
   withr::local_options(list(arrow.debug = TRUE))
+  expect_dplyr_equal(
+    input %>%
+      summarize(counts = n()) %>%
+      collect(),
+    tbl
+  )
 
+  expect_dplyr_equal(
+    input %>%
+      group_by(some_grouping) %>%
+      summarize(counts = n()) %>%
+      arrange(some_grouping) %>%
+      collect(),
+    tbl
+  )
+})
+
+test_that("Group by any/all", {
   expect_dplyr_equal(
     input %>%
       group_by(some_grouping) %>%
diff --git a/r/tests/testthat/test-dplyr.R b/r/tests/testthat/test-dplyr.R
index ed03c58a884..d3a9994b5f1 100644
--- a/r/tests/testthat/test-dplyr.R
+++ b/r/tests/testthat/test-dplyr.R
@@ -26,6 +26,7 @@ tbl$verses <- verses[[1]]
 # c(" a ", "  b  ", "   c   ", ...) increasing padding
 # nchar =   3  5  7  9 11 13 15 17 19 21
 tbl$padded_strings <- stringr::str_pad(letters[1:10], width = 2 * (1:10) + 1, side = "both")
+tbl$another_chr <- tail(letters, 10)
 
 test_that("basic select/filter/collect", {
   batch <- record_batch(tbl)
@@ -961,7 +962,7 @@ test_that("No duplicate field names are allowed in an arrow_dplyr_query", {
       filter(int > 0),
     regexp = paste0(
       'The following field names were found more than once in the data: "int", "dbl", ',
-      '"dbl2", "lgl", "false", "chr", "fct", "verses", and "padded_strings"'
+      '"dbl2", "lgl", "false", "chr", "fct", "verses", "padded_strings"'
     )
   )
 })
@@ -1109,9 +1110,6 @@ test_that("trig functions", {
 })
 
 test_that("if_else and ifelse", {
-  tbl <- example_data
-  tbl$another_chr <- tail(letters, 10)
-
   expect_dplyr_equal(
     input %>%
       mutate(
@@ -1342,7 +1340,6 @@ test_that("case_when()", {
     )
   )
 
-  skip("case_when does not yet support with variable-width types (ARROW-13222)")
   expect_dplyr_equal(
     input %>%
       transmute(cw = case_when(lgl ~ "abc")) %>%
@@ -1355,10 +1352,11 @@ test_that("case_when()", {
       collect(),
     tbl
   )
+  skip("ARROW-13799: factor() should error but instead we get a string error message in its place")
   expect_dplyr_equal(
     input %>%
       mutate(
-        cw = paste0(case_when(!(!(!(lgl))) ~ factor(chr), TRUE ~ fct), "!")
+        cw = case_when(!(!(!(lgl))) ~ factor(chr), TRUE ~ fct)
       ) %>%
       collect(),
     tbl