a node has to own at least 51% stake of all the network.

This is correct. Note: you should own 51% of network, not 51% of emission.

only a single miner can append a block at the same time

Not true, but it does not matter.

how can fork happen to make the double spending attack?

Assume you have large stack.

• backup your database at some checkpoint
• sell your stack for "anything else"
• restore from backup and create a private network which is not connected to main network
• leave your chain mining until the cumulative difficulty become larger than in main network
• connect your network to main net and force it to reorganize mainchain to your chain where you still have your funds and 100% mining rewards

voila

Forking in proof of stake. Like the algorithm outlines, one particular validator is pseudo randomly selected for block addition. But yet there can be forks because:

Say a particular block A is present as root. Now a validator X adds block B. Now Block X has the chain A->B. But if there is network problem in X, the block B might not reach other nodes. So all other nodes have only A. But X only gets the chance to add block for a specified time interval. If the block is not added in that time interval, its chance lapses. So since all the nodes didn't receive B because of the network failure at X, they think the chance of X lapsed and another validator Y now adds block C.

Thus all other nodes except X have A->C where as X has A->B. Later when the network restores, B is found and you have a fork.