breather tube from crankcase or valve cover brings blow-by to the air cleaner to reburn. excessive blow by will be heavy with oil in the air.
Seized engine. Thousands of dollars to install rebuilt engine. Bad news.
Without an oil filter in place the engine oil would just be pumped out of the engine , so the engine would run until the engine seized
There are several reasons your filter may leak. It might be the wrong filter. Did you oil the gasket before installing it. Did you over torque it (more than 1 turn after contact). Did you make sure the old oil gasket wasn't still on the engine block before installing the new filter. Could be a defective filter(bad gasket). In any case, better replace it to be safe, filters aren't supposed to leak. Better spend 3 to 4 bucks now than 3000 bucks later on a rebuilt engine.
Not really worth that much. Plenty of 4.6 L engines around, and at that age, it would have to be rebuilt. Say about $ 150.00 to $ 200.00 for the complete engine, then the cost to rebuild it is a lot more.
High torque starter
Sometimes, depending on the severity of the engine, the block can be plugged or welded. Most of the time it would be quicker or even cheaper to get a used or rebuilt engine.
Sure if the car was worth that and you know the rebuild was done correctly. If you have any doubts walk away. If the engine was not rebuilt correctly, it may not last long even though it may run perfectly now.
Belt
That would all depend on the type of engine that you are looking to get, the condition it is in, the amount of work that has been done to it, etc. There is no real specific price that can be assigned to it. The best thing to do would be to contact a seller and ask around.
On a 2003 Ford Taurus : Yes , there is an engine oil filter On the 3.0 liter " Vulcan " V6 engine , the oil filter would be on the side of the engine that faces the front of the vehicle and takes the ( Motorcraft FL-400-S engine oil filter ) The 3.0 liter DOHC , Duratec V6 engine takes the ( Motorcraft FL-820-S engine oil filter )
Odds are the needle and seat in the carb is faulty. Probably need to be rebuilt.
If it's a gasolene fuelled engine I would use a synthetic, and keep right on using this type of oil after the initial oil and filter change has been done and the break in period is over.