I've received 5 transactions to my electrum wallet, each to it's own never used address. 4 of them have been shown on the wallet balance and in transactions history, 1 not. But, when I checked this address at blockchain and at electrum's addresses section they shown the coins arrived.
1 transaction can pay to multiple addresses. The only explanation I can think of is that 2 of your addresses received their payments from a single transaction which means you see 4 transactions in your history but 5 coins in your coins tab and correct balance in each address.
Next I've sent a little part of the coins from X address to another one also assigned to my wallet but already used address. Same again. Not shown at the balance and history.
This is not possible. If you send from an address from your wallet to an address from your wallet, your balance will not change (except for the small fee deduction) but you will see the transaction in the history tab.
If nothing changed at all, it is possible that you never actually sent that transaction. Either previewed it and then discarded the tx or saved it locally.
I've sent amount which was less than available balance, and much less than available balance + coins from address X.
Make sure you are calculating what you received and what you've sent correctly. It is easy to make a mistake since you've already made multiple transactions here which are hard to follow.