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 ...
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.
In your exact context, the real underlying implication is probably more don't go too fast for your dating partner rather than ...for yourself, but that's just a quirk of the exact context. Normally, getting ahead of yourself doesn't imply being precipitate / over-hasty from the perspective of others.
For example, " She is getting crazy " vs " She is going crazy ". and " I'm getting online to check my Facebook " vs " I'm going online to check my Facebook "? According to my research, it seems that " get " can be used for both positive and negative feelings, for example, " she is getting upset " and " she is getting excited ".