cracked head
you mean there is coolant in the oil or oil in the coolant either ways sounds like a head gasket problem.
Not keeping oil in it, not changing the oil and filter, not servicing the timing belt when it needs it, running it without coolant.
I would say yes, if oil has mixed with the coolant, that's the most probable cause.
It can get in through the timing cover. That does car does not have a "timing belt" cover, but it has a "timing chain cover." There is a BIG difference, as a timing belt cover does not have coolant and oil running through it, but a timing chain cover does have both coolant and oil running through it.
You probably have a cracked engine block and engine coolant is mixing with engine oil.
Not a problem unless you plan on running the engine... Of course it is a problem. An oil filter is mandatory for the life of the engine.
Need more info. Year, engine size and what it is in so I can answer your question correctly. You will have to ask your question again with this information and your problem. Failed oil cooler, headgasket, cracked head, etc.
Can be a hole in the radiator or a problem with one or more of the hoses. A mechanic can run a pressure test to see where the problem(s) are located at.
If it is an automatic transmission, the cooler in the radiator is most likely leaking into the coolant system.
If a vehicle is loosing coolant then there is a leak. If no leak is visible then the coolant could be leaking into the oil, or leaking into a cylinder and being blown out through the exhaust.
Although some intake manifolds do have coolant running through them, none have oil in them. The most common reasons coolant would end up in your oil reservoir ( pan ) is a blown head gasket or a cracked head.
You should able to tell if it's leaking so I assume that you are not seeing any coolant where you park so it's a good chance you got a blown head gasket and the coolant is leaking in your cylinders and being burned off or leaking into your oil. Check your oil after running and if it is foamy it has coolant in it.