You should have done one thing at a time and tested in-between.

SU carbs are less complex and easier to work on than Zeniths so previous owner may have switched in an older SU with fewer hose outlets.

My Haynes manual has a whole section 4B for carbed 240s. It shows the different hose setups and years.

"I injected some fuel into carburator"
If it didn't "catch" then it would be a spark issue. If it did, it would be a fuel issue.

"I've comitted an error leaving a car without oil for all night and than letting it wait few hours before first starting attempt."
It doesn't matter how long you let the oil drain, as long as you filled it before starting it. Even then it would start if it wasn't a fuel or spark problem though it would wreck your engine pretty quickly.

"The crazy thing is that the battery dashboard light stopped to iluminate at this time even that the engine wasn't runnig."
What's the condition of your wiring harness? (Starts at gray plug on firewall.)
It may be that the thin alt. wire (red) is loose.

"after few tries the engine started for like two seconds but didn't let me to get itself on higher revolutions. It happened like 3-4 times "
Check your connections to the ballast resistor. (About a 4" rod with wires at ends, on strut hump of passenger side near wiper motor.)

"I felt that throttle pedal was a lot softer. Then it came back to a "hard one", "
If it was the brake pedal, then understandable as vacuum boost is off when engine shuts down. Don't know about throttle/gas pedal. Maybe it is sticking at the carb?

Anyhow, you should have left opening carb till last and just cleaned the intake with carb cleaner.
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1980 245 Canadian B21A with SU carb and M46 trans