There is no difference between der Schlips and die Krawatte to mean tie, but der Schlips is slightly more colloquial.
Die Mütze = keeps your head warm, soft, you can put in your pocket without damage. (e.g. bobble hat, cap, beanie)
Der Hut = brim all around, made of stiff material (e.g. formal hats like top hat, bowler hat)
There is no difference between das Portmonee and der Geldbeutel to meant purse/wallet, it just depends on where you are. Das Portmonee is most commonly used, especially in North Germany, however der Geldbeutel is second most common.