When quoting words or phrases or sentences

When you are quoting a word or a phrase or a sentence   or using the word/phrase/sentence quoted , is your only option is to put it in quotation (in quotation marks)? Can I slant it when will it be OK?

'Slant it' means put it in italics, I presume.  If you are writing a formal paper, stick to the quotation marks (" ").  If it is a word or short phrase, you can use single quotation marks (' ')-- but also check with the person to whom it will be submitted; some have their druthers.  In less formal situations, italics or underlining often work as well.

Should the sentence in parenthesis have a period in the end after the word "free trade"?

I wouldn't-- it just clutters the sentence.