I used to dry hop in a bag, but then just started throwing them in on their own after hearing about other guys doing it. So far no ill effects. I generally dry hop anywhere from 1 to 2 weeks, but I have dry hopped an amber ale for almost 4 months (not planned, son had health problems and couldn't get to bottling) and the beer came out great. More hop aroma than I had planned, but I liked it. Almost smelled like an IPA or something.
The only issue I could see with just adding the pellets into the fermenter is that you can't take them out, like you could if you put them in a bag. This would come in handy if you want to dry hop for a week, or so but don't want to or aren't ready to bottle when the dry hopping period is done. If they are in a bag you could take them out of the beer, but with no bag they are in there for good. I guess it's your choice, but just remember, if you use a bag, sanitize it before you put it in the beer.
Re: oak chips. I have never used them before, so I don't have any advice. Good luck and let us know how it turns out for ya.