This job’s really getting to me. Idiom "get to grips with" I'm trying to get to grips with the new software. As for your last example: He’s refusing to testify. I think the Mob got to him. You could perhaps explain this as a combination of Arriving somewhere and annoying. Or you could just say it's another phrasal verb with a special meaning.
Which one is correct- He did not succeed to get the job though he tried his level best. He did not succeed in getting the job though he tried his level best. Book says second one is correct.
"are getting married" implies either already arranged event or certainty in the future (Try saying "they are [definitely] getting married" ), whereas "be going to" sounds to me like a prediction or, even, an alternative to "will", yet does not sound like a decision made at the moment of speaking.
To Get is the normal form and would be best for everyday use. However book titles are allowed artistic license. Regarding the to Getting forms, I would think of it this way: 1) The Essential Guide to (doing something) + (which is) Getting Your Book Published and 2) The Guide to (doing something) + (which is) Getting it On In these examples each phrase can stand on its own, but you have follow ...
Yes there is a difference. Trees are getting cut down refers to an action that is in progress. Someone is cutting the trees. It is the form encountered more frequently. Trees getting cut down can be used in the context of an intended action. To explain: If someone has decided to cut some trees down, they may be referred to as the trees getting cut down. The trees are still standing at the time ...