Future tense in relative clauses

[ringu20]

For example,

"I need a key that will open the door."


Can I omit this sentence like "I need a key opening the door." or "I need a key to open the door"


Would both sentences be correct?

Can we omit relative clauses that include future tense? Or can't they be ommitted?

 

[abaka]

"I need a key to open the door" correctly expresses the key's purpose and your intent.

The phrase "a key opening the door" describes a key that is just now opening the door: to be precise, in the throes of doing it. But even so, it's an awkward phrase; say rather, if you must, "a key that is opening the door". It seems inappropriate here.

I can't answer your questions about the omission of future tenses in relative clauses. It's fruitless to look for general rules where none exist.