How do I determine if a column name exists in an array or datasubset?

You can store the result of the todatasuset into the local variable & print the same variable on the screen. It will list the detail info of it.

If I understand your question, I think comparing index( local!varName , "xyz" , null() ) to null() might help.

What about using fn!contains(array, value)? See the below test code.
= load(
local!datasubset: todatasubset(
{
type!Column(
field: "username",
alias: "un",
visible: true
),
type!Column(
field: "firstName",
alias: "first",
visible: false
),
type!Column(
field: "lastName",
alias: "last",
visible: true
)
},
a!pagingInfo(
startIndex: 1,
batchSize: -1,
sort: {
field: "alias",
ascending: false
}
)
).data,
{
a!textField(
label: "Test column exists or not",
value: if(fn!contains(local!datasubset.field,"lastName"),
"The column exists",
"The column is missing"),
readOnly: true
),
a!textField(
label: "all columns",
value: local!datasubset.field,
readOnly: true
)
}
)

I think you might want to know how to check if a datasubset contains a column to show on the screen. Since you set batch size is 2, so only 2 columns will be shown. If so, you can do it in the following way.
= load(
local!datasubset: todatasubset(
{
type!Column(
field: "username",
alias: "un",
visible: true
),
type!Column(
field: "firstName",
alias: "first",
visible: false
),
type!Column(
field: "lastName",
alias: "last",
visible: true
)
},
a!pagingInfo(
startIndex: 1,
batchSize: 2,
sort: {
field: "alias",
ascending: true
}
)
).data,
local!displayColumns: local!datasubset,
{
a!textField(
label: "Test column exists or not",
value: if(
fn!contains(
local!displayColumns.field,
"username"
),
"The column exists",
"The column is missing"
),
readOnly: true
),
a!textField(
label: "all columns",
value: local!datasubset.field,
readOnly: true
)
}
)

You may wish to include an index to handle null data subsets:

if(
          fn!contains(
                    index(
                              local!displayColumns
                              "field",
                              {}
                    )
                    "username"
          ),
          "The column exists",
          "The column is missing"
),