I can sometimes hear my pulse in my ear. Does this mean that I am having an aneurysm?

No. It is pretty common for people to hear a "pulse" in their ears. If anything it is more consistent with a blockage in the carotid arteries...Not an aneurysm. If it persists, it would be worth while getting a carotid ultrasound to evaluate the arteries.
You might try. Cleaning your ears out with hydrogen peroxide and a bulb syringe.
Not necessarily. It doesn't necessarily mean that you have an aneurysm. But you should have your blood pressure checked along with a complete physical. High blood pressure can cause an aneurysm to rupture if one were present.
Most likely not. Many people can hear their pulse as the carotid artery runs through the temporal bone where the ear is located also. Aneurysms are unlikely to occur in that location but there are situations of congenitally aberrant vessels such as persistent embryonal arteries. Such unusual plumbing can bring the artery close to or even into the middle ear so it may be worthwhile considering a vascular study.