Student or Learner
Is verbless clause and/or absolute clause a formal style of writing ?
A verbless clause is a bit of an oxymoron, given that a clause is defined as a phrase containing a verb. Really it should then be called a phrase. These kind of sentences play havoc with some theories of grammar which say there must be a verb in a sentence, and the verb must have a subject. There was a good example here recently.
The lower the suction load on the air filter of a vehicle, the higher the quantity of air supply to the engine. This would have been written in a journal or similar publication. So I would call it formal.
Absolute Phrases are used a bit like sentencial modifiers. They are also used in formal writing. Just do a search for absolute phrase to find lots and lots of examples.