> Does proof-of-stake generally mean the more money you have the more influence you get over the consensus?
Ethereum does not have on-chain governance, so having more stake doesn't grant you more influence over the network or the rules of its consensus algorithm. What it gives you is a higher probability to be called to do your duty as a validator and get rewarded for it. But what that duty entails is defined in the protocol and implemented in code.
> If yes, how could this manifest itself if a bad actor had a lot of ETH and tried to manipulate the chain?
You would need to get 33% or 66% of the total stake to be able to do some damage. With 33% you can prevent the network from finalizing, i.e. agreeing that a block is part of the forever history of the network. With 66% you could write wrong blocks and make them part of the forever history of the network. The protocol has on-chain mechanisms to deal with the first situation but there are no on-chain mechanisms to deal with the second one and a solution would require social consensus off-chain.
> Could they theoretically jump favored transactions to the front of the line and/or charge less fees for their own transactions?
Anyone creating a block is free to order the transaction however they please and decide which ones are included. You cannot not charge fees, though. To use the network you have to pay certain amount of ETH and this amount gets spent or burnt as it's also referred, it simply disappears from existence.
> How does this affect mining pools?
They disappear, there is no more mining.
> Is a 51% attack any easier/harder/different?
Different and harder. Different for some of the explanations above (the % necessary are different and what can be done at this thresholds also changes). Harder because it's much much more expensive to acquire the stake necessary to attack, so the chain is more secure. But also because an attacker will get its stake slashed (destroyed) and will not be able to do it again. While in PoW, once you have the hashrate you can keep attacking the network ad infinitum or until the rest of the network gets more hashrate than you. It's as if an attacker in PoS would gets mining rigs burnt. PoW cannot do that because it delegates its security to an activity outside the chain (burn energy with specialized HW), but in PoS the stake is on-chain so there are more tools to deal with nefarious actors.
> Does proof-of-stake generally mean the more money you have the more influence you get over the consensus?
Ethereum does not have on-chain governance, so having more stake doesn't grant you more influence over the network or the rules of its consensus algorithm. What it gives you is a higher probability to be called to do your duty as a validator and get rewarded for it. But what that duty entails is defined in the protocol and implemented in code.
> If yes, how could this manifest itself if a bad actor had a lot of ETH and tried to manipulate the chain?
You would need to get 33% or 66% of the total stake to be able to do some damage. With 33% you can prevent the network from finalizing, i.e. agreeing that a block is part of the forever history of the network. With 66% you could write wrong blocks and make them part of the forever history of the network. The protocol has on-chain mechanisms to deal with the first situation but there are no on-chain mechanisms to deal with the second one and a solution would require social consensus off-chain.
> Could they theoretically jump favored transactions to the front of the line and/or charge less fees for their own transactions?
Anyone creating a block is free to order the transaction however they please and decide which ones are included. You cannot not charge fees, though. To use the network you have to pay certain amount of ETH and this amount gets spent or burnt as it's also referred, it simply disappears from existence.
> How does this affect mining pools?
They disappear, there is no more mining.
> Is a 51% attack any easier/harder/different?
Different and harder. Different for some of the explanations above (the % necessary are different and what can be done at this thresholds also changes). Harder because it's much much more expensive to acquire the stake necessary to attack, so the chain is more secure. But also because an attacker will get its stake slashed (destroyed) and will not be able to do it again. While in PoW, once you have the hashrate you can keep attacking the network ad infinitum or until the rest of the network gets more hashrate than you. It's as if an attacker in PoS would gets mining rigs burnt. PoW cannot do that because it delegates its security to an activity outside the chain (burn energy with specialized HW), but in PoS the stake is on-chain so there are more tools to deal with nefarious actors.