Please guve clear explanation with necessary diagrams and proper steps for the questions

Let D1 be the DFA defined by the following diagram (using the alphabet ={0,1} : Your friend claims that D1 recognizes the language L00={0s0s{0,1}}, (that is, the language of all binary strings of length 2 or longer that start and end with 0s). They provide the following argument to support their claim: Choose a string tL00.t must be of the form 0 s 0 for some binary string s. When D1 processes 0s0, the first step will move from state a to state b. If s has any leading 1s, it will stay in state a while it reads those 1s, and when it gets to the first 0 in s (if it has any), it will move to state c. Once D1 gets to state c, it will stay in state c for the rest of the string because all transitions from c lead back to c. If s doesn't have any 0 s, then the DFA will stay in state b until it reads the final 0 in t=0s0, at which point it will finally transition to c. Either way, when D1 finishes reading t, it will be in state c, which is an accept state, so D1 will accept t. What is wrong with this argument? (Note: Providing a separate argument that D1 does not recognize L00 can be part of your answer, but you also have to explain what mistake