In the currently ongoing elections, do I need to cast all 3 votes for my votes to count, or is casting say, one vote or two votes, also counted ?
No, technically you do not have to vote more more than one candidate for your vote to be counted. However, it is highly recommended that you do so!
SE elections use what is called the STV (Single Transferable Votes) method of tallying votes. This is a system specifically designed to minimize wasted votes when electing more than one candidate at a time out of a large pool. Basically what happens is that your votes cascade from one candidate to the next as they get elected.
The single transferable vote (STV) is a voting system designed to achieve proportional representation through ranked voting. Under STV, an elector's vote is initially allocated to his or her most preferred candidate, and then, after candidates have been either elected or eliminated, any surplus or unused votes are transferred according to the voter's stated preferences. [...] It [transfers] votes to other eligible candidates that would otherwise be wasted on sure losers or sure winners.
Your vote will not carry any less weight by voting for more than one candidate, and in some cases might even carry more weight. In this particular election, three candidates will be elected, so even after you've done all you can do for your absolute favorite candidate, you can still influence the other choices. If your candidate loses, your vote for them as first choice will still have carried full weight. If they win, your votes for the other candidates will be made even stronger.
By voting for more than one candidate, you can make your opinion heard even in the case that your first candidate loses. If you vote for some dead beat that has no chance at all, your vote will be taken into account ... but because it wasn't enough to get them into office, it is then moved down the chain to your next preferred candidate, giving your favorite runner up a chance of beating somebody else's first choice.