Does tylenol (acetaminophen) thin blood like aspirin?

No. Mechanism of tylenol (acetaminophen) not exactly known but it is not considered an anti-platelet medication and so does not cause an increased tendency to bleed unless overdose occurs and liver function is impaired. Liver is responsible for many clotting factors. Routine tylenol (acetaminophen) does not predispose to significant bleeding risk.
No. Aspirin affect platelets to thin the blood, tylenol (acetaminophen) does not, but if someone develop liver disease due to tylenol (acetaminophen) toxicity, the liver damage can lead to coagulation problems (blood thinning).

Related Questions

Is there any common (otc) drug/medicine like aspirin or tylenol (acetaminophen) that will kill you in high doses?

Everything. In high enough doses, essentially every medicine becomes a toxin / poison. There is a toxicology book that addresses this: "the dose makes the poison.".

Which is safer for the body if used occasionally: tylenol (acetaminophen) or aspirin I've tried both, feel like I've had similar results with both that's why?

Depends. It depends on whether or not you have any other health conditions. Generally, because of aspirin's effects on the stomach, tylenol (acetaminophen) is considered safer as long as you don't have any liver problems. If you don't have stomach problems (i.e., ulcers, bleeding, etc.), though, occasional use of either should be fine.
Both. Acetominophen (tylenol) intake should be limited to less than 4 grams daily. In excess, liver damage may occur. Aspirin can trigger asthma attacks, GI bleeding, allergic reactions, and intake should be limited to less that 3 grams daily. Occasional use and alternating them may be best.

Is it ok to take tylenol (acetaminophen) and aspirin together for a headache?

OK but. For headcahe it is better to space tylenol (acetaminophen) and Aspirin 4 hours apart. Instead of Aspirin consider Aleve : it's longer acting (up to 12 hours).
Sure. You can space them out or choose one of the combination products like Excedrin (aspirin, tylenol (acetaminophen) and caffeine). I also agree that Ibuprofen is a better choice than aspirin.

Can I take tylenol (acetaminophen) with codeine if allergic to aspirin?

Yes. Tylenol (acetaminophen) and Codeine are totally different drugs than aspirin. You should be fine taking these medications.