What does this mean? Are this also different stable coins with the same name?
Yes, they are. The difference is each network.
-Can it theoretically be, that a tether on Ethereum blockchain can have another value than the one on Solana blockchain? And does the arbitrage ensure that these two tethers have the same value?
Possible, but the price difference doesn't allow arbitration for small amounts due to network fees. Also no CEX that pairs trades against one brand of coin just because it supports multiple networks.
-Can it theoretically be, that for example the tether on Ethereum blockchain has lost confidence and becomes worthless, whereas the one on Solana blockchain still has more confidence?
Possible, if one of the blockchains (somehow) stops working due to a network attack or smart contract exploit.
-Or is it technically (by design) impossible, that a tether on one blockchain has another value than the one of another blockchain?
Same answer as the 2nd one