How does Punisher provide his needs

I mean safe houses, nutrients, weapons, ammos and other things

Writers don't explore that kind of things nowadays. But back in the day he used fake alias like Frank Rook, Charles Fort and others to purchase stuff like safe houses and other stuff. He financed his war with the criminals money. For the weaponry he got his own weapons dealers and some weapons he collected from criminals he killed.

he steals from the dealers/murders to fund his war

yes also he has a lot of military connections from when he served. from time to time they help him out with medical attention, guns, supplies, intel, etc...