1) Is correct in the query with

 ?protein up:reviewed true .

2) The query in the Q. does not return anything for taxon:3702 as there are no rdfs:subClasses for Aribidopsis Thaliana, it is a leaf node. This means the entry is directly linked to that taxon instead of via it's ancestors. This is fixed by changing the query slightly to deal with both the ancestor and direct case (both sides of the UNION below)

    VALUES ?taxonlist { taxon:3702 taxon:562}
    {
        ?taxon rdfs:subClassOf ?taxonlist .
        ?protein up:organism ?taxon . 
    } UNION {
        ?protein up:organism ?taxonlist . 
    }

3) we use the cross reference section which are done via rdfs:seeAlso . But as there is the possibility of more than one KO per entry we group them with a subquery.

OPTIONAL {
    SELECT ?protein (GROUP_CONCAT(?ko; SEPARATOR=", ") AS ?kos)
    WHERE{
      ?protein rdfs:seeAlso ?ko .
      ?ko up:database <http:
    } GROUP BY ?protein
}

4) to use the existience/evidence for concept at Protein or Transcript level we add

{
     ?protein up:existence up:Evidence_at_Protein_Level_Existence .
} UNION {
    ?protein up:existence up:Evidence_at_Transcript_Level_Existence .
}

5) To make sure the entry is annotated as an enzyme. We use the same subquery idea as for the KO links but now not OPTIONAL. To make one value of the many potential ECs we use a subquery with a GROUP_CONCAT. The long line with up:enzyme is the different ways uniprot links an ?ec to an entry.

SELECT ?protein (GROUP_CONCAT(?ec; SEPARATOR=", ") AS ?ecs)
WHERE{
  ?protein up:enzyme|((up:component|up:domain)/up:enzyme) ?ec
} GROUP BY ?protein

Combing it in one query gives

PREFIX up:<http://purl.uniprot.org/core/>
PREFIX taxon:<http://purl.uniprot.org/taxonomy/>
PREFIX rdfs:<http://www.w3.org/2000/01/rdf-schema#>

SELECT 
    ?protein 
    ?taxon 
    ?name
    ?kos
    ?ecs
WHERE
{   
    ?protein a up:Protein .
    ?protein up:reviewed true .  # have to be reviewed        
    ?taxon a up:Taxon .
    ?taxon up:scientificName ?name .
    VALUES ?taxonlist { taxon:3702  taxon:562 }
    {
        ?taxon rdfs:subClassOf ?taxonlist .
        ?protein up:organism ?taxon . 
    } UNION {
        ?protein up:organism ?taxonlist . 
    }

    {
        ?protein up:existence up:Evidence_at_Protein_Level_Existence .
    } UNION {
        ?protein up:existence up:Evidence_at_Transcript_Level_Existence .
    }
    {
       SELECT ?protein (GROUP_CONCAT(?ec; SEPARATOR=", ") AS ?ecs)
       WHERE{
           ?protein up:enzyme|((up:component|up:domain)/up:enzyme) ?ec
       } GROUP BY ?protein
    }
    OPTIONAL {
        SELECT ?protein (GROUP_CONCAT(?ko; SEPARATOR=", ") AS ?kos)
        WHERE{
            ?protein rdfs:seeAlso ?ko .
            ?ko up:database <http://purl.uniprot.org/database/KO>
        } GROUP BY ?protein
    } 
}

Which is testable at sparql.uniprot.org.