Why can't it be "purse"?
Does diese not also stand for these?
Yes, but "these" is plural and "Tasche" is singular (one bag). The plural would be "Taschen", therefore "These bags" is "diese Taschen".
does anyone have tips for not mixing up 'deise' und 'Deine'.... I could use some help...
There is no word deise.
And diese can mean either "this" (before a feminine noun) or "these".