About the first order logic (valid, Unsatisfiable, Syntactically wrong)
1 uses a function symbol Processor which is not in the logic signature. Hence, it's outside the syntax.

4 tries to equate a proposition with Speed(MyPC). You can't equate propositions in FOL. Outside the syntax.

3 is not universally true for every function Speed and every argument MyPC.
For instance interpret MyPC as the natural $0$, and Speed as the successor function to obtain $\mathsf{succ}(0)=0$ which is false. Hence the formula is not valid. However, it is satisfiable: now interpret MyPC as zero and Speed as the identity function to obtain $\mathsf{id}(0)=0$ which is true. The formula has a model and a countermodel: satisfiable and invalid.

2 ∃ x ( Speed(x) = Speed(MyPC) ) is always true, since we can take x to be MyPC. This holds no matter how we interpret Speed and MyPC. Hence is it valid. (Alternatively, we can even show it is a theorem of FOL using a proof system, and then rely on the correctness theorem to claim it is valid.) Since formula 2 is the negation of a valid formula, it is unsatisfiable.