You can invest from the phone. Don't think I've actually used a real computer once. Go to the LCS website. BAWSAQ is hit or miss, and it seems to be down more often than not.
Personally, I've really sucked at investing, although part of that is the interface being pretty crappy. The graphs in particular are awful, and don't update very well. It also appears that the LCS stocks are fairly scripted. The evidence suggests that influencing a company's competition doesn't actually effect stocks, unless it's part of a story mission. You can blow up all of the Post-Op trucks you want, and it won't effect Go-Postal. There does appear to be evidence listening to a station you invest in has a positive effect, and the more claims you can cause for the insurance company the more money they'll make (I guess they're crappy and don't ever pay out on them).
Also, most of the stocks you pump and dump will rebound. Once you cause a company's crash, buy it back when they bottom out if you're interested in a long-haul investment.