In this case, spelling out the number is a short cut to not to write out the the trailing zeros that make up that number. For the first sentence "...an extra thousand" and "...an extra 1 thousand" are equivalent statements however, colloquially thousand means one thousand, which means 1 thousand is redundant. This isn't found in formal writing, this used for informal writing. If you were writing a formal article or essay or argumentation you should do 1 thousand and 1 billion, or probably more properly one thousand and one billion. And for extra clarity you can do, One [1] billion dollars. And One [1] thousand dollars.

In general it is not advisable to mix up numbers as words and as figures. However, news reports put space and readability at a premium so some unusual abbreviations are common. 1) In the first sentence, you can write "an extra $1K" . I have never seen " $1 thousand". 2) If you are writing a news report, you can put the $1,2,3 before "million", "billion" and "trillion", but not usually before "hundred", "thousand". 3) If you are writing a bank cheque or legal document, you will be well-advised to use figures 0...9 at one place and words "one, two, three million dollars" at another place nearby;this is done to eliminate the possibility of confusion/fraud. 4) The preceding "an extra" has no effect on the way you choose to write it.