@hosseinimr93 is 100% correct.
I just wanted to address your very specific question completely:
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I want Electrum to be installed in 2 places at the same time, both will be online. If I change the password of the first installation, what happens to the second one
--snip--
The (short) answer: nothing
The (long) answer (slightly simplified):
When you use the same recovery seed to create 2 wallets on 2 devices (as mentioned by hosseinimr93), both devices will use the same master private key (since this master key is calculated using only the seed phrase, not the password).
This master private key is used to derive private keys, the private keys are used to calculate public keys, the public keys are hashed to create addresses.
In other words, both wallets will contain the same private keys/addresses. If you fund one of these addresses, both wallets will update/increase their balance. If you spend an unspent output funding one of the addresses managed by your wallets, the balance of both (identical) wallets will decrease.
It's a difficult concept for new members... Most new members think the wallet actually stores your bitcoins... This is not true... Bitcoins aren't anything physical. Your balance is actually just the sum of unspent outputs funding addresses whose private key(s) you controll. These unspent outputs are registered on the decentral ledger: the blockchain. So, your two wallets actually only contain keys to spend unspent outputs that are registered on a decentral database.
Your wallet is merely a "window" to the blockchain. It's a nifty tool that parses the decentral database for you, and sums up all entries funding an address that is controlled by your wallet. So, both wallets can contain the same keys, and offer the same "view" of the blockchain.
The password is used to encrypt your wallet file... But the wallet files itself should contain more or less the same data (i say "more or less" because you can also store metadata, like labels...)
@hosseinimr93 is right tough: it's not a good idear to use the same seed phrase for a mobile and a desktop wallet. If you lose your mobile, or if your seed gets compromised because it was on an insecure device, you'll lose all your funds!