The first issue is caused by dealing with keyword offset. It is allowed as table alias and that leads to a conflict. 

Right now the best what you can do is using simple variables or constants. This should work.

 e.g. the following query:

SELECT /*+ first_rows(25) */

                 api.patient_ot (patient_nr => p.patient_id

                                ,afdelings_code => p.afdeling_id

                                ,naam => p.naam

                                ,voornaam => CASE l_tonenvoornaam WHEN 1 THEN p.voornaam ELSE null END

                                ,geslacht => p.geslacht

                                ,geboortedatum => p.geboorte_dt

                                ,email => p.e_mail

                                ,rijksregister_nr => p.rijksregister_nr

                                ,gsm_nr => p.gsm_nr

                                ,adressen => NULL)

                ,COUNT (1) OVER ()

        BULK COLLECT INTO l_patientlist.items, l_rowcount

        FROM dl.patient p WHERE 1=1

        AND (p_naam is null OR p.naam LIKE p_naam)

        AND (p_voornaam is null OR p.voornaam LIKE p_voornaam)

        AND (p_patient_nr is null OR p.patient_id = p_patient_nr)

        AND (p_rijksregister_nr is null OR p.rijksregister_nr = p_rijksregister_nr)

        AND (p_geboortedatum is null OR p.geboorte_dt = TO_DATE(p_geboortedatum))

        AND (p_afdelings_code is null OR p.afdeling_id = p_afdelings_code)

        ORDER BY p.voornaam, p.naam

        OFFSET (l_patientlist.page - 1) * l_patientlist.limit ROWS

        FETCH NEXT l_patientlist.limit ROWS ONLY;

When putting the expressions in a variable it works fine.

However, It usually does not make sense to use the row_limiting_clause without ordering the result. And since you asked for a workaround...

SELECT naam
  FROM dl.patient
 ORDER BY naam
OFFSET 10 ROWS
 FETCH NEXT 3 ROWS ONLY;

Using a subquery works as well: 

SELECT * FROM (SELECT naam FROM dl.patient) a
OFFSET 10 ROWS
 FETCH NEXT 3 ROWS ONLY;

SELECT naam
FROM dl.patient
OFFSET 10 ROWS
FETCH NEXT 3 ROWS ONLY;

When using OFFSET/FETCH I am getting following error:

4-Blocker: no viable alternative at input '('

This is not supported by PL/SQL Cop ? If no, is there any workaround ?

1) typed "ut", crtl-tab, selected a template

2) right click, selected "Check"

3) typed "ut", ctrl-tab, selected another template

So using them does not seem to be a problem. But when I open "Preferences" as you've mentioned, no code templates are shown. Looks like a bug. Strange.

As a workaround, never save code templates in the preferences after "Check". Restart SQL Developer before changing code templates. Then you shouldn't lose them (again). Not nice, I know, but at the moment I have no better idea.

I am encountering following problem: after I perform a check with PL/SQL Cop for SQL Developer I can not use my code templates anymore. When I open Preferences -> Database -> SQL Editor Code Templates all the code templates are gone.

When I restart SQL Developer everything is ok again, but when I try to add a new template first the configuration is corrupt.

Is this a known issue ?