It doesn't. Verification of Electrum only ensures that the binaries are compiled and verified by ThomasV. You're still trusting ThomasV and someone else unless you review the codes yourself. Vulnerabilities can be put intentionally or unintentionally.

You're still obtaining the SHA256 hash from the site and that is the point for MITM attacks to happen. PGP is better since you're validating against an identity so you just have to make sure that the chain of trust is not compromised.

Not as far as I know of. Humans aren't the best at generating entropy anyways.
You can generate a large amount of addresses at once.

wallet.create_new_address(False) for i in range(X)

Or increase the gap limit.

When you generate a seed in electrum, you are technically generating every address that will ever be used in your wallet. The private keys are calculated from your seed. So if you have two computers that are not connected to the internet, and create wallets with the same seed on both computers, both will “generate” the exact same addresses in the exact same order.

When generating a seed, you need to be sure that the seed is in fact random. As long as you are certain your computer can generate random numbers that are truly random, an authentic version of electrum should generate a random seed.

You can compile electrum yourself so you personally know what it is doing when generating a seed. Or you can generate a seed yourself.

You can set the gap limit in electrum to higher than the default for your electrum client to display more addresses.

Some people would say yes. Others would say that you shouldn't trust anyone.

Such incidents have always been due to user error - generated on an internet enabled machine, seed phrase stored insecurely, etc. - and not due to an Electrum error.

As ranochigo points out, unless you review the code yourself, you are going to have to trust someone, whether that is the developer or the community who are telling you it is safe. If you do not have the required knowledge to review the code yourself, then this is what I would do -

Download and verify Ian Coleman's site
Download and verify Electrum
Run both on a permanently airgapped machine running a clean OS
Flip a coin 256 times and enter the entropy in to Ian Coleman. It will generate a seed phrase for you
Double check your coin flips against the BIP39 wordlist in groups of 11 to make sure the seed phrase generate matches your entropy
Enter the same seed phrase in Electrum
Check that the addresses provided by both Ian Coleman and Electrum match

This allows you to ensure the entropy is random, the seed phrase matches the entropy, and the addresses match the seed phrase, all without requiring any review of the code.

The cost of being paranoid is much bigger. So now I must trust visual studio for compiling me the source code?

Okay I think that will just verify electrum with kleopatra. No one had ever an incident with that. Then I'll simply turn off internet connection forever and I will generate some thousands of addresses.

Thank you.

You are not obligated to use electrum, there are a lot of wallets and electrum is not ideal for all things. this wallet will fail if you want to generate thousands of addresses/transaction daily because it is not intended for that.

For thousands of daily transactions you need more numbers, I can think of the following:

Server: (hot wallet)

 - use blocknotify to updates balances to external database.
 - Script to check balance and update it (manually) if your hot wallet balance is less than X amount and move it (Auto) if your hot wallet balance is more than X amount.

cold wallet: (Offline)

 - use Armory wallet that holds the private keys.
 - Admin access to refill your hot wallet.

And if you don't trust the developers, do it yourself: You need cryptography library that supports secp256k1 ECDSA, generate your private key and use it to get your public key or  Bitcoin address (SHA256 and RIPEMD-160)

you can start with this topic:
How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
What is Elliptic Curve Cryptography? Understand how is it related to Bitcoin

Why would you spend the time flipping a coin 256 times to only create a single address, when the exact same 256 flips could be be used as entropy for a HD wallet to create a seed phrase and therefore create as many addresses as you want? If you follow my instructions in my previous post you can use this coin flipping method to create an entire wallet. Then just keep that wallet permanently airgapped and export the xpub to a watch only wallet on your internet-enabled device.

This method also means you get a seed phrase, which is significantly easier and safer to back up than a bunch of individual private keys, and you can also avoid any issues with change addresses and address reuse.

I would not say it is a given that you should not trust someone under any circumstances. Better advice for the OP would be to direct him to use his own judgement and resources to decide if ThomasV should be trusted or not. Being that electrum is very widely used (this would not apply if it were not), the OP can search for reports of there being problems with electum loosing coin.

Most bitcoin users lack the technical expertise to understand electrum's source code if they were to compile it, and this is simply not realistic to expect 'normal' non-business users to do this.