Simple question really, considering theres a very small group of miners controlling the chain ATM.
Miners are distributed around the world, many of them may join the same mining pool to even out the variance in payouts though. Do not confuse the number of mining pools for the number of miners. Really, it is not possible to know the number of distinct mining entities that exist.
Whats to stop them from being forced by the goverment to disallow certain transactions or just mining empty blocks
Nothing. If a certain govt could reliably regulate any miners within their jurisdiction, then they could perhaps enforce a rule like this.
The good news is, since hashing power is distributed, no one govt can censor the chain in this way. If Govt-A decides to censor transactions, it won't affect any miner that exists outside of Govt-A's control, and so while the transactions in question may take a little longer (on average) to get confirmed, this won't censor them outright.
In fact, the miners existing under Govt-A's rule will now likely become less profitable, as they will be unable to mine the transactions that are sanctioned by Govt-A. This means all other miners will become more profitable for it - the system is self-balancing in this respect.
Or even worse, whats to stop a country like china from just investing massive ammounts of money into unbeatable mining pools and destroying every appearing coin that way?
The majority-attack (51% attack) is a well-known attack that is possible against the network. An attacker with a majority of hashpower could censor transactions indefinitely, but there is a caveat: doing so requires a HUGE investment of capital, and then a HUGE ongoing electricity cost, for the entire length of time the attack is maintained. Further still, once the investment into the specialized computer hardware is made, an entity could mine profitably instead of spending money to attack the network. This is a heavy financial incentive - perhaps some government would be willing to ignore this, but it seems unlikely for an attack to be sustainable (and indeed, we have a decade worth of evidence of a system that works as intended, and has not been attacked in this way).
Excellent reply. I'd just like to note one important aspect. Mining pools control which TX's go into blocks. So, even though the pool participants are scattered (we don't know how scattered though), the concentration of mining power into less than a dozen pools is cause for concern. I made a quick spreadsheet from data from blockchain.com and over 70% hashrate is in Chinese pools. – Jose Fonseca – 2019-10-16T11:27:02.157
@JoseFonseca that is a good point, and there is work being done to remedy that exact problem. For example see BlueMatt's BetterHash protocol, it allows the individual miner to generate the block template (and thus pick transactions), even if they are mining as part of a pool: https://github.com/TheBlueMatt/bips/blob/master/bip-XXXX.mediawiki
– chytrik – 2019-10-17T04:59:47.367