"Paint the pie in the sky " means what?
I've never heard anyone say that, and I've never come across it in writing. The phrase "pie in the sky" means a goal, plan, desire, etc. that is completely unreasonable and unattainable. "The company president assures us that the firm's profits will be much higher than last year, so we'll all get nice raises in pay. But that is just
pie in the sky because the products we manufacture are rapidly becoming obsolete."
The word wherewithal, why is it meant money?
You mean "why
does it mean money?"
It does not refer to money exclusively. It can be used for any resource needed to perform a task. "Our company would love to build a factory in your town and provide jobs to your citizens, but the wherewithal for this project is not available. There are no forests nearby for wood, your electric company's output is too small to power a factory, and your roads are too narrow for the semi-trailers to carry the products to market."
"Put a thumb in the pie but not to bake it " means what?
I've never heard that, sorry. Perhaps it's a British or Australian expression. The only reference of which I'm aware that touches on this is in the ancient nursery rhyme, "Little Jack Horner." A little boy puts his thumb into a pie and pulls out a plum. This is very rude behavior. And of course, the pie had obviously already been baked!
Dither and waver means the same?
"Dither" applies only to human conduct: inability to make a choice. "John wants to go to two concerts, but he only has enough money for one ticket. He's been
dithering about which one to buy, but if he doesn't decide soon, the tickets will be sold out and he won't be able to go to either one."
"Waver" has a more general application. "The daily high temperature has been wavering between 65 and 75 degrees, this week." (Sorry, we Americans use the Fahrenheit scale, not Celsius.) "The frequency of the radio signal from the fort keeps wavering, so we can't hear everything they're trying to tell us."
And yes, "waver" can also apply to human decisions, but it does not usually mean that the person is quite as foolish as if he were truly dithering. "The coach had to decide whether to put John into the game or George. He wavered for half a minute and then chose George."
"Have your back to the wall " means what?
It's a reference to fighting. If your enemy keeps charging and you have to keep moving backwards to avoid losing the fight, you may eventually discover that your back has hit a wall, so you can't retreat any further. You have to fight harder or surrender.
"Dog " can be a verb. Why dog?
Dogs are famous for not giving up a pursuit. If a dog discovers a lizard and the lizard runs away to safety, the dog will keep chasing the lizard until he catches it, or until he is out of breath.
This is not a totally accurate description of dogs' habits. Most dog breeds are not distance-runners, and can't follow prey for more than a few minutes. They're more likely to use their extremely good sense of smell to follow their prey. Only a few types of dogs can run for a long time, and most of them were bred to chase predators away, such as the various types of wolfhounds, and the Anatolian, a gigantic animal that protects livestock from lions.
However, whether he does it by running or by smelling, a dog will not give up a hunt. That's what to "dog someone" means.
Inter means bury? Is it very less used?
That's a very formal word. It's used by funeral directors, since the family of a dead person doesn't want to think of him being "buried" in dirt. They'd rather hear the word "inter." No one uses it in ordinary speech or writing, unless they are specifically referring to a funeral. The word is from Latin
in terra, meaning "in the earth."
Cause celebre is a word borrowed from where?
When in doubt, bet on French.

It means "famous case." Remember that the French conquered England in 1066, and French was the country's official language in government, business and education for several centuries. And by the way: they never left. They just started speaking English. Nonetheless, French was the primary language used in diplomacy, the arts, science, government and education throughout most of Europe, up into the 1800's.