The distribution of clausal complements is limited in English. Some verbs only take infinitives, while others only take clauses, and some can take both.
1) "Request" can take a 'that' clause.
2) This is ungrammatical, and I don't think any native speaker of English would say it. It is acceptable in other languages and the default in Greek, for example.
3) This is acceptable. It's a little more formal than an infinitive, but both are fine.
4) Certainly the 'that' clause is acceptable. The use of the subjunctive is a little weird here. "would take" is much more natural, or also "took" (the past subjunctive).