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SPIN is not the obvious choice here - domain-specific tools dedicated to protocols are more suitable. Some examples can be found here: Tools for modelling and analysis of cryptographic protocols

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Short answer: No, it is not vulnerable to man-in-the-middle attacks, assuming that Alice and Bob each have the right signature verification key of the other party. Yet, the man-in-the-middle attack could have taken place at the moment of exchanging the signature verification key. So if $sig_{X}$ is party X's signature key, the attack on the exchange itself ...

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Here is how it can be Vulnerable. Alice: $x$ Bob $y$ Eve $z$ Alice$\rightarrow$ $g^x$ $\rightarrow$ Eve->$g^z$->Bob Bob$\rightarrow$ $g^y$$\rightarrowEve\rightarrow g^z$$\rightarrow$Alice What Alice thinks key is $g^{(xz)}$ what Bob thinks the key is $g^{(zy)}$ Eve can compute both of these values $(g^x)^z$ and $(g^y)^z$ This is why we need ...

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It is secure against private key exposure but not against replay attacks by Eve. A three-way protocol avoids this, and doesn't need to use timestamps. The description below is from Delfs and Knebl's book Introduction to Cryptography. Each user, say Alice, has a key pair $(e_A, d_A)$ for encryption and another key pair $(s_A, v_A)$ for digital ...

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