Know this is an older post, but just wanted to say that on my LG900g I had the same issue with downloaded getjar apps not working etc. They have a choice for the LG900g on the site, but seems like some of the apps don't work with this phone. Using the LG GW300 choice seems to bring up more apps that download correctly and work.
I have a 4gb card in the phone so I download to the computer and then copy them to the card using the USB connection. By the way, at least on my computer, the pop up box that comes up showing the folders etc on the phone is the one for the phone itself, not the memory card.
I prefer to keep the phone memory as clear as possible and so put everything I can on the memory card. What I have to do is go to "My Computer" and the phone shows up as two USB connected drives with different letter designations. I click properties on them to find the one that is the 4gb memory card and then open that one to copy apps etc. too.
Once done and the phone is safely removed then you just click on the phones menu, go to the program you just loaded on and click it. With mine I go to My Folder and then option down to the Other tab and click on that. Then just a matter of highlighting and clicking the program you just loaded on the phone. The install takes just a moment.
Oh, and I'm using Opera Mini 4.3 with good results. There is a signed version that is Opera Mini 6, but I've not tried that one. When I put in the phone model (believe I used LG GW300) the Opera Mini site said that their testing had concluded that the 4.3 version was the optimum. Only thing a bit annoying about it is that you have to click to confirm you want to continue when accessing sites. The pop up that comes up says something about how additional data costs may apply.
Anyway, hope that helps someone. Cheers