Well, it'll be harder to remove, but the real problem is that too much thermal paste will make heat transfer worse (too thick). The whole idea of thermal paste is to force out air from being trapped in between the HSF and proc (air is a horribly poor conductor), however thermal paste isn't really as conductive as most people think.

Your HSF mounting may have shifted, and the contact is not not as good as it was originally. Nothing to to with thermal paste.

Alcohol or spirit works well too if you're looking for a cheap alternative.

For some reason, CPU temp and Core 1 & 2 temps are usually not the same. The only reason I can think of is that the CPU temp is from a sensor underneath the CPU (on the mobo) while the Core is the thermal diode in the CPU. That way the sensor outside will register a cooler temp than the core.

There is something seriously wrong either with your sensor or the software you're using to read the temp. Or you are from somewhere really cold..like siberia..

Well, I use spirit and cotton wool. Tissue alone isn't recommended, but in a pinch it won't really cause any serious problems.

Thinner also works wonders on tough removals, better than nail polish remover (aka Acetone), but like nail polish remover leaves an oily residue you must clean off with alcohol.