I noticed that near the stem there is a little hole with something in it, do I just press that with a tweezer or something and the stem comes out ? Also what position should the crown be ? Functioning, date or time setting ? That little hole doesn't seem to have a screw in it but a tube. Is this right ?
The detent on this model of Omega is spring loaded. You describe a "hole". The attached image is from the Ranfft archive, and shows the Omega caliber 613. Note the call out pointing at the detent button which is not a "hole", but a post with an indent in it. Pull the stem all the way out to the hand set position, then press that button, andpull the stem out. Now that you have it out of the case, what are your intentions? Too nice a watch to destroy by ill-advised experimentation!
My intent is to clean the inner case, the old rubber gasket left some marks on the metal. Relax. I'm good with my hands, and I'm not exactly a noob. I just wanted to be sure what I have to do. When inserting the stem back in, will I just push it in all the way or must I again lightly press the detent button as I push it in ?
Probably safest to press the detent button down when you re-insert the stem. Watches such as this one generally don't require this step as the leading edge on the land of the stem is chamfered to press the detent aside when putting the stem back in. But if the sliding pinion were to shift out of position, you'd be in for a sizeable job to remedy the problem.