However if your Electrum wallet were to be connected to malicious Electrum servers, they could serve you invalid transactions which you would not know are invalid. Said transaction can be included as part of a block; the merkle root would be correct and the PoW of the block would be valid. BUT the block would contain an invalid transaction.
No, that block header would not be included in the block header list that ends in the last currently published block. There's no way a malicious electrum server can tell me that a given transaction is in the block chain that ends in the known recent block on which miners are working now.
As I said before, there's no way to make me another block header list than the correct one, that ends in the recent block headers. I only need to know ONE SINGLE number from the miners: the recent block header hash. That single hash proves to me that any block header list that ends in that hash, is the actual, right one. And nobody can lie to me as to any included transaction. Not even with 90% of all hash rate. Because there's only ONE SINGLE BLOCK CHAIN that can end in this hash, if the hash function is not broken.
This doesn't even have anything to do with proof of work.
You give me the last header hash, and nobody can lie to me as to anything included in the block chain. Because you cannot lie in a linked list of hashes, you cannot lie in a Merkle tree, and you cannot lie about the hash of a transaction.
Mathematically: even without PoW: if you have two block chains, B and B', build of a chain of headers which contain each the top of a Merkle tree of "data segments", and the top hash of the header list of B is equal to the top hash of the header list of B', then B is identical to B'.
If two tops of header lists are identical, the two lists are identical (up to same length, you could append BEFORE the genesis block, true...). If the header lists are identical, the roots of the Merkle trees are identical. And if two Merkle trees are identical, the data segments they hash are identical..