Etc. is a Latin abbreviation. It stands for the Latin phrase et cetera. (Although the Latin is two words, it is usual, though not necessary, to write it as one word in English: etcetera.) This means "and others of the same kind", though when used in English, etc. can mean "and the rest", or "and similar things", etc. Even though the literal meaning is "and others", etc. can be used even when the meaning is "or similar things".
As etc. is an abbreviation, it should be written with a full stop, even when the sentence continues. Some academics insist on this, and some spellcheckers prefer it. The use of etc. this way is decreasing - "particularly in Britain", according to Wikipedia []. (This may be because it saves [infinitesimal amounts of] time and ink to omit the full stop.) Student writers should take note of the prejudices of their readers - and where no such prejudice is expressed, develop their own personal style, and preferences.
It used to be quite common to write the abbreviation with the ampersand, &: &c, logically enough. The great writer on English usage H.W. Fowler and the playwright G.B. Shaw usually printed it thus, towards the end of the nineteenth and in the first quarter of the twentieth century; it is rare to see it now other than in handwritten notes, where it is convenient for some hands.
It is a mistake to write
and etc.The abbreviation already contains the "and".