This is a proverb that has some other wordings. Anyway, this is my first time to read this wording. At the end, it serves the main meaning.

To answer your questions clearly, it would be better to give you the background of the main idea beyond this proverb.
Another wording reads:
سألوا البرص بتنفخ في النار ليه، قال بربي عداوة
the gecko was asked why do you blow the fire, it said I make enemies

This proverb is coined by Egyptian based on a part of a Prophetic Hadeeth (saying) that:
When Nimrod threw Ibraaheem [Abraham] (may Allah exalt his mention) into fire after the latter refuted their false belief by fair argument, all animals and insects used to put out fire with exception to gecko which used to blow up fire...

Then, people spun a proverb depending on this part of Hadeeth. the main point of the proverb is that when a weak ineffective person does a malice that will not even harm the offended person only to prove that he is there and he is too significant to have enemies. You can understand this from the fact that the blowing up of fire by the gecko is something trivial.

Back to your 2nd question, بخيت with shaddah ّ on the خ is derived from بخخ which means spray, sprinkle, etc. because it, i.e., geck sprays this salt from its mouth into something

Hope this helps