You can't reduce them, because when the relative clause has an external subject, a non-finite form of the verb has to be used (such as the present participle or past participle). But the modal verb "can" is defective and lacks non-finite forms. It's true that "be able to" is commonly used as a substitute for the infinitive of "can." But "being able to" cannot be used as a substitute for the present participle in relative clauses; it sounds awkward to native speakers. However, you can use adjectives that have similar meaning as a substitute.
Your example sentences don't sound very natural, and the meaning isn't totally clear, so I'll list slightly different ones.
- One day, a person who can complete this task will appear. (unreduced)
- One day, a person able to complete this task will appear. (uses "able to" + plain form)
- One day, a person capable of completing this task will appear. (uses "capable of" + -ing form)
Regarding the second set of questions: in general, distinctions of tense are neutralized in reduced relative clauses, and the perfect aspect cannot be used. Your options are to not reduce, or to lose this information (or to shift it to the main verb). Since the tense of the unreduced relative clause is different for that of the main verb, the best choice is to not reduce.