Usually, you place the adjective before the noun in the sentence, no matter if it's the subject or not. So, in your example, it would be "shiroi neko" (shiroi, not shiro; shiro is a noun). This rules holds true in most cases, but it depends on the situation.
As for your particle question, it would take pages and pages to explain in detail, but
de is basically used to identify a means, as in "basu de eki ni ikimasu" I go to the station by bus. Sometimes, de can be used to identify the location where an action takes places, but that's more complicated.
dewa is not a particule, but a conjuction. It's main use (in my experience) is in closing a conversation or letter. Again something rather complicated to explain.
wo or o is used to link the object to the verb, as in "eiga wo miru" I watch/see a movie. This is only used when necessary and often skipped in daily converstation.
ni is another doozy. ni often indicates direction, as in where your going. Eki ni ikimasu. I'm going to the station. But this can also be illustrated by "e" as in "eki e ikimasu", which means the same. It is often used in the passive voice as well. Another subject of length.
I suggest you look up a Japanese text book if you're really keen on learning more, but even the best books doesn't explain it perfectly... I've been living in Japan for years now and still have trouble keeping my particles straight...