I don't understand how to use live split properly. How can I start the timer exactly on zero with a negative time? And is it normal if livesplit don't pause the timer while loadings if I start the timer after the 1st loading?

When you right-click LiveSplit & press Edit Splits, there's a section "Start Timer at" you can put that to minus if you want to do what I did. You have to manually start the timer, so it's not accurate and has to be re-timed after a new PB.

No, that's not normal. You have to activate SourceSplit - again, go to Edit Splits, and change your game name to "Half-Life 2 Mods". A text should appear "Game Time and Auto Splitting are available" - press Activate and go to Settings. There, see that Auto Split checkbox is enabled & Game Time Method is "Engine Ticks with Pauses".

Also, remember to compare against In-Game Time on LiveSplit.

If you still have questions, go to https://discord.gg/sourceruns and a channel called #hl2-mods or #source-help.