q.xq

let $results := 
(
let $keywords := ('Money order', 'Creditcard', 'Personal Check')
for $keyword in $keywords
  for $item score $s in doc('xmark')//item[
    payment contains text {$keyword} all words using stemming using case sensitive
  ] (: As expected, I'm not sure what 'score' does. The definition in the BaseX documentation uses the defined term in the definition, so it's very unclear. :)
(: the score is an internal ranking of hits, similar to TF/IDF (term frequency / inverted document frequency), in short: terms that are contained often in a node but rare among all nodes are more important than terms that are generally contained in almost all nodes :)
  order by $s descending
  return <item ranking= '{ $s }'>{ $item/payment/text() }</item>
)
(: $s is unclear to me because score is. :)
for $result in $results
  group by $val := $result/text() (: $val is undeclared.  Where did you find this? :)
                                  (: $val is assigned as part of the grouping specification, we group by $result/text() and name this variable $val :)
  order by $result[1]/@ranking descending
return $result[1]

q2.xq

let $keywords := ('Cash', 'Personal Check')
for $keyword in $keywords 
return <keyword name="{$keyword}"> (: This is actually unnecessary, as one of the returned rows contains the keyword. :)
{
for $result in //item/payment
  group by $payment-method := $result/text() (: $payment-method is an undefined variable.  How does BaseX know where it is referenced from/what it corresponds to? :)
(: sorry, my bad: $payment-method will contain the text() value of each payment item found in //item/payment :)
  order by count($result) descending (: Why do you want to count them? :)
                                     (: we return the most often used payment method first:)
return element {"item"} { (: What's an 'element'?  I'm trying to return the values of 'person', 'payment type', 'amount', etc. :)
     (: the element operation constructs an XML element node, in this case:
        an <item /> with an attribute count -> e.g. <item count="1" />
    :)
    attribute {"count"} {count($result)}, (: What's an attribute?  Would this be like lang="eng" in <cd lang="eng"></cd>? :)
    $payment-method
  }[. contains text {$keyword} phrase] (: What contains it? :)
}</keyword>