How do you show that the following languages are decidable? Also why the language halts and is a decider must be explained. I'm only posting two sub questions from the overall question as I would like to know how to do the question rather than just get an answer. I would like to use the process used in solving these two problems to solve the rest of my problems.

Show that the language { | A is a DFA and L(A) is not empty} is decidable.

Show that the language { | A and B are Turing machines and they produce the same output on their tape for a given string w} is decidable. For this question simply construct a Turing machine. You do not have to show that the machine is a decider for the language.

Another thing that confused me was that the second question just asked for a Turing machine to show decidability, does that mean you just make a Turing machine for the problem before it and then just explain the machine? A step by step on how to do problems like these would be appreciated.