If I make changes to the keywords and headers on my homepage will that cause any down time or search ranking changes?
I think If you are making major change like removing or adding new keyword will have major change in SERP. but if you are changing the place of the keyword, adding s(es) may have no major change in SERP. i don't know what other webmasters think about that let's see others opinion that may have any conclusion.
definately ranking will down, bcoz current result will give you good ranking in google so you make it mind that old keywords should be there
I also agree with the rest. It will definitely affect how crawlers identify your site and thus will cause difference in search engine ranking position. But bear in mind, it's not always for the worse. Who knows maybe it might be for the better. There always a risk but if you think it's worth changing, then go for it.