I have problems to understand what is the difference between the serial number of a certificate and its SHA1 hash. 

The MSDN says: 


  Serial number   A number that uniquely identifies the certificate and
  is issued by the certification authority.


So can I identify a certificate by its serial number, right? 

Wikipedia says for the hash:


  Thumbprint: The hash itself, used as an abbreviated form of the public
  key certificate.


So the hash identifies the (e.g. RSA) key.

I currently do some research on Android app certificates and I found some interesting certificates:

[Issuer][Serial][SHA1 Hash][Valid From]
[C=US, L=Mountain View, S=California, O=Android, OU=Android, CN=Android, E=android@android.com][00936EACBE07F201DF][BB84DE3EC423DDDE90C08AB3C5A828692089493C][Sun, 29 Feb 2008 01:33:46 GMT]
[C=US, L=Mountain View, S=California, O=Android, OU=Android, CN=Android, E=android@android.com][00936EACBE07F201DF][6B44B6CC0B66A28AE444DA37E3DFC1E70A462EFA][Sun, 29 Feb 2008 01:33:46 GMT]
[C=US, L=Mountain View, S=California, O=Android, OU=Android, CN=Android, E=android@android.com][00936EACBE07F201DF][0B4BE1DB3AB39C9C3E861AEC1348110062D3BC1B][Sun, 29 


And there are a lot more which share the same serial, but have different hashes.

So there can be a certificate with different key? Who is actually creating the serial number when creating a certificate for an Android app? For the hash it is clear, but can I create a new certificate with the same serial number as another cert?

Can I be sure that a certificate with the same serial number was created by the same person?

In a certificate, the serial number is chosen by the CA which issued the certificate. It is just written in the certificate. The CA can choose the serial number in any way as it sees fit, not necessarily randomly (and it has to fit in 20 bytes). A CA is supposed to choose unique serial numbers, that is, unique for the CA. You cannot count on a serial number being unique worldwide; in the dream world of X.509, it is the pair issuerDN+serial which is unique worldwide (each CA having its own unique distinguished name, and taking care not to reuse serial numbers).

The thumbprint is a hash value computed over the complete certificate, which includes all its fields, including the signature. That one is unique worldwide, for a given certificate, up to the inherent collision resistance of the used hash function. Microsoft software tends to use SHA-1, for which some theoretical weaknesses are known, but no actual collision has been produced (yet). A collision attack on SHA-1 has now been demonstrated by researchers from CWI and Google.

(The thumbprints you show appear to consist of 40 hexadecimal characters, i.e. 160 bits, which again points at SHA-1 as the plausibly used hash function.)
