You are absolutely allowed to remove it, you just have to replace it. The correct thickness is "try to wipe it all off with kitchen tissue", it really shouldn't be a grease hazard to clothes.

Also washing up liquid should do the trick.

Eggs pretty much work like meat when it comes to stickiness, just with an even tighter window when it comes to right temperature and it's even more important to let the thing be for a while before attempting to move it.

Also, yes, scraping. I use a burger flipper spatula which practically has a knife edge at the front. Ideally though things should be moving when you shake the pan, that is, loosen on their own.

As for the "you can't clean it" it's BS in and of itself. I use a chainmail scrubber to remove the big stuff, then soap and one of those green scrubbers to get it good and clean. The trick is, no matter how you clean it, you need to dry it COMPLETELY (I use paper towel) then oil it immediately. Doesn't take much oil either, maybe a drop about the size of a nickel for a 12" skillet. My wife has alpha-gal syndrome, so all cookware needs to be thoroughly cleaned with soap and water, no exceptions.

Once you get a good seasoning set in, it's almost indestructible, unless you seriously mistreat it... and even then it's fixed pretty easily with an SOS pad, oil, and an hour or two in a hot oven.

My cast iron is more non-stick than any so-called 'non-stick' pan I've had, and I have one of those The Rock pans. I think the only caveat is you have to get a decent one. Anything made in China is no good (nothing necessarily about the casting or finish of the pans themselves, they just have very low quality iron); I personally buy Lodge, but there are a few other good brands to look in to.