Yup, if you're doing the DONEx ticket, ignore the 34k limit. The OW site doesn't have the best user interface, it should make it more clear that you'd be over the mileage for a Global Explorer ticket, but perfectly ok for a OneWorld Explorer ticket. BTW, Australia & Oceana count as a continent, so what you have is already a DONE4, if you add South America it'll be DONE5. Looks like you have 14 segments right now, since IST-BCN isn't a non-stop as far as I know. but you can do that on QR BTW instead of IB (IST-DOH-BCN), you'd only have 2 segments left over so have to choose GRU or EZE, not enough to include both unless you drop something in Europe, for example just go to MAD and drop BCN and take your own domestic flights or train internally. There's also no longer a OW flight between GRU and EZE so that would be a surface segment (which sadly still counts towards your 16).

Lastly if you do go to South America a lot of the connecting flights going toward LAX will be at MIA... that's a horrible airport to clear into the US at, so allow PLENTY of time, and also be careful selecting the MIA-LAX flight as only some of them have Flagship service and real business class seats. JFK is the safer choice on both accounts if the times work and far better lounge while waiting.

Regarding earning status, sure you'd be able to but just be aware that some programs have minimum metal segments in addition to the mileage. AS, BA, QR, and JL come to mind there. Where do you live and who do you fly with most in OW, who would you benefit most from having status with? If AA you have to keep in mind that all AA, BA, and IB segments have risk of very minimal mileage earning, they may or may not credit as distance (which is what you want on this type of ticket), there's lots of discussion about that in the AA forum.
Just your itinerary as you have it now is about 32,500 base miles before any cabin bonus or elite bonus comes into play (the later of which you'd have zero to start but would kick in at each status level going up). Thrown in JFK-GRU-JFK before LAX and it takes you to 41,200 base miles, before cabin and elite bonuses. But you have a lot of IB, BA, and AA segments in there which is the unknown if crediting to AA.. But that's plenty of miles to earn mid-tier if not top tier in some programs after cabin bonus comes into play. AS would be super easy IF you can meet their AS metal requirement, you'd be WELL in excess of the MVP 75 threshold but need 12x AS metal (and coded) flights per year to maintain.

http://wheretocredit.com would be useful to evaluate some differences, just look at earnings for D class on the flown carriers.