Is {∅} ⊆ ∅ true?
I don't think so, because If ∅ is a subset of every set (also ∅) ∅ ⊆ A it means that no elements are a part of any set, but in this case {∅} ⊆ ∅ must be true if every element in A is an element in B, B is just an empty set that not contains elements.
Am I right? Thanks
It is not true.
So the outcome of your thinking on this is correct. Unfortunately I have troubles in following the thinking itself expressed in your question, and the fact that it is quite a story makes me suspicuous.
More concise you can say: $\{\varnothing\}$ has an element, and if $\{\varnothing\}\subseteq\varnothing$ is true then this element will also be an element of $\varnothing$.
This however is absurd, since by definition $\varnothing$ has no elements. We conclude that $\{\varnothing\}\subseteq\varnothing$ is false.