The first two words are pronounced the same but have distinct meanings. An official group that deliberates, like the Council on Foreign Relations, is a “council”; all the rest are “counsels”: your lawyer, advice, etc. A consul is a local representative of a foreign government.
These are sometimes interchangeable, but when you are stressing similarities between the items compared, the most common word is “to”: “She compared his home-made wine to toxic waste.” If you are examining both similarities and differences, use “with”: “The teacher compared Steve’s exam with Robert’s to see whether they had cheated.”
People who use the shortened form are often convinced they are right because they are being “ironic” and some even claim it’s the original form. But here’s the entry in The American Heritage Dictionary of Idioms:
This expression originated about 1940 in Britain and for a time invariably used couldn’t. About 1960 could was occasionally substituted, and today both versions are used with approximately equal frequency, despite their being antonyms.
“I could care less” just isn’t logically ironic. The people speaking feel irony, but their words don’t convey it. “I’d buy those jeans” could be ironic if you really meant the opposite: you wouldn’t buy those jeans if they were the last pair in the world. But “I could care less” isn’t used to imply its opposite: that you care more. Thus it is not ironic.
“Couldn’t care less” is a strong statement because it says you don’t care at all, zero!
“Could care less,” whatever meaning you take it to have, does not have that crucial message of zero interest which gives the original saying its sting.
The popular salad made of shredded cabbage was originally “cole slaw,” from the Dutch for “cabbage salad.” Because it is served cold, Americans have long supposed the correct spelling to be “cold slaw”; but if you want to sound more sophisticated go with the original.