AE86 4age engine not starts crank ok backfires to air intake

[Ryo]

I can try external fuel pump in canister if this helps but still i think i am fighting with two or three problems as i mentioned after longer cranking the engine it starts but like on 3 cylinders with really noisy lifters but will not hold idle i must keep it on gas after the engine gets warmer it starts an all 4 cylinders and it runs stable. No trouble to start the engine immediatelly when warm. Plugs are always wet from fuel. Also it sometimes fires into air intake when starting and i already see some dirt in air filter probably fuel (AFM still okay as i tested it in my AE86 last time). Now i don't know which way i should proceed as i think fuel delivery is still working but feels like something is clogged. And i remember i smell fuel as well in engine oil as oil level was above dipstick so i needed to drain it to normal level. Engine oil was all dark as well. Engine oil is Eneos 10W40 was changed only about 200km back when we tried to drive a car a little. The problems started after battery was changed for new one and engine oil changed. As i mentioned before car was not started for about 4 years and was parked outside in summer or winter. The fuel is not old as we drained the old one and put new inside already. Fuel filter was still not changed and injectors have been not cleaned yet i only inspected their sound with screwdriver. Was iaming to clean them but still not sure if mine problem is in fuel delivery as when engine is hot it runs well and i can rev it than without any issue.