This all depends one the processor model used. Some processors have built-in acceleration for certain cryptographic primitives; AES-NI is one you mentioned that exists in Intel processors.
Even then, whether the HDD would be faster than the processor depends on the CPU and the HDD, and the CPU usage at that time.
And does this apply to the hash algorithm?
The hash algorithm is used to derive the symmetric key, so it will only make a difference at the time you unlock the volume. Afterwards, the key is stored in memory, and the hash isn't used anymore.
Or is a drive encrypted with Serpent as fast as one encrypted with AES-Twofish-Serpent?
No; as the last mode is actually a chained system, it will have to decrypt or encrypt the data sequentially. Whether you will actually notice the overhead is a different question though. It might or might not matter for you.
Could machines with a processor with AES-NI decrypt my serpent-HDD as fast as an AES-HDD ?
AES-NI only accelerates AES, not serpent. Whether the one will outperform the other can only be benchmarked; you might want to try a program such as