As title states, is the checksum for bc1 adresses the same as for 1.. / 3.. adresses? It seems that it isn't supported by sites like these
They are not the same. In fact, bc1 addresses use a completely new encoding scheme known as bech32. This is specified in BIP 173[/quote] and designed specifically for Segwit. Bech32 addresses and Base58 addresses are completely incompatible with each other.How can i verify myself manually if a bc1 adress is valid?
Not really.Is it actually any different?
Yes, they are very different. Instead of a checksum based on the hash of the data, it is a BCH-like error correcting code. This lets it both detect errors and tell you where they are, as well as correcting some of them (if there are fewer errors than a certain threshold). 
