If someone manages more than 50% of the mining power, this situation necessarily compromises the integrity of the past blocks and newly generating blocks?
The integrity of past blocks is not necessarily compromised. However, their finality may be compromised. If the miner is not malicious, then there is only a fear of attack. For example, a single miner (or, more precisely, a pool) has had more than 51% of the mining power on Bitcoin, but AFAIK, there were no changes to historical blocks on the Bitcoin blockchain that were a intentional result of possessing a majority of hashing power.
If the miner wants to revert and is unlucky, finality is not compromised. If the miner wishes only to censor, then the miner does not care about blocks from before the initiation of the attack.
Thus, possessing a majority of hashing power and enough time are necessary conditions for rollback (statistically), but not sufficient.
Note that we can detect a rollback resulting from a 51% attack. We can also determine how much time an attacker would be expected to expend to reverse transactions.
Yes. This is called a 51% attack.
Since the longest chain of blocks is always considered to be the most trustworthy, the attacker with 51% could create the longest chain first, thus doing what they want with that blockchain.
The security of the blockchain rests in that achieving 51% computing power is very difficult since there are many different actors in the network with differing interests.
In a blockchain that uses a proof-of-work consensus algorithm, if someone can take the control over more than 50% of mining power (generally called a 51% Attack ) it's possible to make a longer chain that would eventually be accepted by other nodes as well, as you have correctly guessed. Good reads on this can be found here and here.
In order for the attacker to make his blockchain the longest, he would need to have more computational power than the rest of the network combined in order to catch up (hence, "51% attack")
But what is important is it's even possible to attack a blockchain network even with less mining power than 50%, which is called selfish mining. In that you manipulate the network by selectively publishing the blocks. You may refer this post for more detailed explanation. But as one of the comments says uncle-inclusion reward mechanism in ethereum discourages selfish mining.
There are no steps taken to stop selfish mining in Ethereum (indeed, it is impossible stop an actor's ability to mine selfishly). However, the uncle-inclusion reward mechanism is an economic incentive against selfish mining; it stops being a net incentive if the miner has means of profiting from selfish mining other than block rewards
However the possibility of 51% attack is inherited in a proof-of-work type consensus algorithm. A good analysis on security measures to overcome 51% attack can be found in this question. If you are more concerned about security of a blockchain, security comparison of Proof of Work and Proof of stake in this answer might help you as well.