Yup. The penalty is not kept by anyone though, it’s burned. Once your balance drops to 16 ETH, you’re removed from the validator pool. This happens slowly and depends on many factors of the current network.
It depends. In addition to the impact of effective balance there are two important scenarios to be aware of:
Being offline while a supermajority (2/3) of validators is still online leads to relatively small penalties as there are still enough validators online for the chain to finalize. This is the expected scenario.
Being offline at the same time as more than 1/3 of the total number of validators leads to harsher penalties, since blocks do not finalize anymore. This scenario is very extreme and unlikely to happen.
Note that in the second (unlikely) scenario, you stand to progressively lose up to 50% (16 ETH) of your stake over 21 days. After 21 days you are ejected out of the validator pool. This ensures that blocks start finalizing again at some point.
If your validator isn't online and/or not able to "do its job" in the allowed for time-period, then it will be penalized.
The penalty for missing one validation is small; the penalty for missing a block proposal is also not huge, but bigger than the penalty for missing a validation. Penalties would pile up over time if a validator is offline for an extended period.
Long story short: if you intend to run an ETH2 validator, you should be reasonably sure it will be able to run well-connected to the Internet for extended periods of time. Intermittent and brief periods of downtime would not have a substantial economic impact on your validator, but extended periods of downtime would be bad.
