You can display them for the amount of time you wish. Since you put them on yourself, you can also remove them. To vote simply click on the flower beside them photo. You'll see the flower change from orange to grey, denoting a vote by you. Later when you view projects they will continue to show grey, since you voted.
Butterfly, the projects seem to stay on 'forever', which is terrific beacause it means that newcomers, and oldies, can browse through them, and glean ideas. The flowers are a fun way of saying you like someone's project. I'm not sure why it says 'vote' when you hover over them, I think it just means vote to say that you like that project, not as in any sort of competition. The comments are for the same but when you want to make it more personal, or ask a question about it. You can give a flower 'and' write a comment if you like, I do that quite often, I love giving people flowers, and here's one for you and Mops. So really it's your choice how you tell people that you like their project. Hope this explains things. Enjoy giving flowers and writing those comments, I know I will.
I have no idea how long projects stay on, but since I first visited the site no projects seem to have been taken off. The maker can take it off herself. Voting is either a comment or giving a flower. Significance of the flower here is 'well done' I think, but without typing in a comment.