Homomorphic crypto allowing anonymous yes/no votes? I'd need a crypto system allowing online yes/no votes but without revealing who voted what. Is a "partial" homomorphic crypto system what I'm after? Would, for example, Damgård-Jurik work in my case?

In my scheme there would be a server getting the votes and the server shouldn't see who voted what. However we can consider that the server shall not cheat: he won't modify the voting results. But the votes should still be anonymous.

If I need homomorphism, how does it work? Does each voter need to get the encryption from the previous voter? Or can the centralized server receive all the encrypted votes and then "mix" them himself and, once mixed, get the result?

How does it work it there are say, four voters: does the scheme break if only three people vote?

For example I played with the nice simulator here, which expects 8 voters. You can't put seven voters on that page: is this just an implementation detail of that site or is Damgård-Jurik expecting all the votes from a number of voters known beforehand?

Also the page shows who voted what, but it's not clear to me if it's for instructional purposes or if, when the vote counts happens, the votes aren't anonymous anymore.
A homomorphic cryptosystem has some operation $*$ on ciphertexts that correspond to some other operation $\circ$ on plaintexts, that is
$$\mathcal{D}(c_1 * c_2) = \mathcal{D}(c_1) \circ \mathcal{D}(c_2).$$
Typically, the ciphertexts you get by applying $*$ look like ciphertexts that are produced by the encryption algorithm. For Damgård-Jurik, $*$ is multiplication modulo $n^{s+1}$ and $\circ$ is addition modulo $n^s$.

A cryptosystem is secure if the ciphertext does not help you to say anything about the message encrypted.

Suppose you encode "yes" as $1$ and "no" as $0$. The voter will encrypt his encoded vote and send it to the server. Suppose the server receives ciphertexts $c_1, c_2, \dots, c_L$ that are all encryptions of $0$ or $1$. The server can now multiply the ciphertexts to get a single ciphertext, which by the above requirement will satisfy
$$\mathcal{D}\left(\prod_i c_i\right) \equiv \sum_i \mathcal{D}(c_i) = \text{number of "yes" votes.}$$
The server can therefore find the correct election result by decrypting the product ciphertext.

It does not really matter how many ciphertexts are submitted.

If the server is passive (honest-but-curious, will try to break confidentiality without deviating from instructions), the voters are honest and the cryptosystem is secure, the server cannot deduce anything about the votes from the ciphertexts (except the result, of course, since he decrypted a ciphertext containing the result). Damgård-Jurik is generally believed to be secure.

The interesting question is of course what happens when the voters aren't honest or the server tries to cheat. There's a lot of nice cryptography in the answers to those questions.