Could you help me please as I haven't found a direct rule. 

" Whether or not"  - is it possible to use Future tenses after this structure? 

1. Let's see whether or not I accomplish /can accomplish my goal. 

2. The Russian economy will survive whether or not EU expands/will expand its sanction.

  Is it the same rule as using "whether" and thus, can be considered as conditional sentences?

Can you give me some other conditional structures  please. 

We will go to the beach if it is sunny. (not if it is raining, snowing etc)

We will go to the beach unless it is raining. (The only thing that will stop us is rain, so fog or snow is fine!)

We will go to the beach whether it is sunny or not. (Basically, we plan to go whatever the weather conditions are like).

Thank you, James :)

Graham,

Thank you very much. I'd like to insert some "hearts" to express my appreciation for your constant help :-)

One more example.

I will help you if you agree. (I will help you with your permission)

I will help you unless you disagree. (I will help you unless you openly say you do not want help)

I will help you whether you agree or not. (I know you need help and you are being polite or stubborn and I decide not to listen to your opinion)

Yes, whether is generally a type of conditional in its grammatical form.