A relative clause is a clause that modifies a noun or noun phrase.
Can a relative clause modify a noun and a noun phrase at the same time?
Example 1
An ripe apple that has been cut into pieces and rice that are going to be cooked together should be prepared right now
that are going to be cooked together is a relative clause.
A ripe apple that has been cut into pieces is a noun phrase.
rice is a noun only.
Can the relative clause modify An apple I bought yesterday and rice at the same time?
There is no rule that prevents this, but your specific example is so complicated that it would be considered poor English.
English, like every other natural language, has a recursive structure, for example a noun phrase can contain a clause that contains a noun phrase. There is no rule for saying how deep and how complete this kind of structure can go. But beyond a certain point, it becomes increasingly incomprehensible. As an aim of good English is to communicate, pushing what is possible in grammar so it hard to understand is not a good idea.
A good principle to apply is is "end weight". Place longer and weightier elements at the end of sentences. A fault in your sentence is that it violates this principle by forming an overly long subject.
Applying those rules, and making a few minor modifications gives:
You should now prepare a chopped apple and some rice that you will cook together.
