Bought cheap airfare to Barcelona, now what?

You have more than enough time to plan this.
Just get a guide book on Spain and read it to pick the sites you want to see based on your own interests .

Pickpocket type crime in Barcelona: similar to other European cities or much worse? Will likely avoid the Metro and will not be doing any nightlife activities.

This is overstated; don't be scared to go out in the evenings. The Spanish day starts and ends a lot later than in America. You will see kid and families out pass 11pm. That is just the way it is.

You are more likely to be robbed in Boston; it is more dangerous and would have more violent crime in comparison to Barcelona.

Yes, definitely enough time.
Will read guidebook advise and research that more than is needed I am sure by the time the dates come but only so valuable as I am fine not seeing everything and not trying to devise an exact day by day plan just general guideline.

I value more personal feedback and often run itineraries by the forum especially when first planning them to get initial feedback. Has been valuable for me in the past to tweak my thoughts ; realize I need more days here, can skip this, etc... Until I form something firm enough to book those inter flights and start reserving some cancellable lodging.

I will be in Barcelona in two weeks for 3rd time.
It might be easier for others if you list the days of your proposed itineraries like this instead of writing it in sentences:
Barcelona
Barcelona
Barcelona
Barcelona
Barcelona
Fly to San Sebastian
San Sebastian
San Sebastian
etc.

Then after you get feedback and settle then you buy whatever transport tickets, and then you decide what to see and do.

Good to hear about the pickpocket issue being overstated.
I did not mean to imply I catered my plans due to the issue.

Our usual travel plan is no nightlife regardless of location ; be out for sunset/dinner as usual but usually not out very late and usually out early each day to see areas while the tourists are still sleeping is the time I enjoy cities the most.
Avoiding the metro is also just something we often do, opting to take cabs despite the higher cost for the convenience if on a short trip to a city like Barcelona.
Would take a bus as needed to a location or a train if to Monserret of course.

Yes good plan to list out how you have suggested. Will work on that, still in the very early stages at this point in time.

Well you're in luck! Not sure about your exact dates, but you may be in time for Barcelona's annual Major Festival, La Mercè, which is during September 21-24. The festival itself is huge, there are 100s of events spread throughout Barcelona's squares, streets, museums, and parks.

The best part - all the entertainment is free! This is something that we put on for ourselves, not just for tourists. If you want to experience Catalan culture like a local, at least for a few days, this is a great opportunity. I would highly recommend you shoot for at least a couple of days in Barcelona during the Mercè festivities

Now let's say best case you have 8 nights available, min 4 nights in Barcelona. You could visit the Basque country with those other 4 nights, as you mentioned, but it will be quite tight to include two extra major cities, Bilbao/San Sebastian including the countryside, to your itinerary. Not sure if those two metropolises will fulfill your non-city atmosphere requirement.

Mallorca (either spelling is fine), is also a good option and should have less tourists in late September, I'd probably pick that option, with a base in Palma. Or for a more off the beaten path island consider Menorca (Mallorca's smaller brother), with a base in Mahon.

You could also stay closer to Barcelona, there are plenty of areas that would be of great interest to a landscape photographer (no need to hop on another plane):

Mighty Pyrenees Mountains: Ribes de Freser, Queralbs, Vall de Nuria, La Cerdanya

Medieval Catalonia: Girona, Besalú, Pals, Rupit, Ripoll

Turquoise Costa Brava: Cadaqués, Ancient Greek ruins of Empúries, Tossa de Mar, Calella de Palafrugell

We were in Madrid, Granada and Barcelona in June, and I was pleasantly surprised at Spain. It was relatively inexpensive and the people there were quite beautiful. Two of our stops were staying in apartments with great a/c and laundry facilities.
My wife liked Barcelona so well, she went back last month with her daughter.
When I travel to any new city, first thing I do is go to Wikipedia and read about the city in detail.

I am not fond of mid-trip flights, especially on as short a trip as this, and you are planning on three of them. I take it that you have done this before and are OK with spending three days doing the airport dance? You are starting out with 12 full, relatively non-jetlagged days by my counting. Now three of them are going to involve traveling to and from airports. So you'll only have 9 days when you can relax where you are or perhaps take a day-trip that requires only an hour or so (one-way) on a train.

I definitely would not go to Sicily for just a few days. For me it's a 2-to-3 week destination (or longer), so to me taking two flights in order to have such a short visit would not be a good idea.

I hope to finally get to Mallorca myself this year and will probably be there for 6 or 7 days. Splitting 7 or even 8 night between Barcelona and Mallorca (losing a good chunk of the travel day) feels tight to me, but 4 nights/3 nights or 4 nights/4 nights wouldn't be crazy since you are not interested in Barcelona's museums.

It's too bad the Basque Country doesn't have super-fast rail service from Barcelona. There's currently a direct 5-1/2 hour train to San Sebastian leaving at 7:30 in the morning. That might be as good as flying, depending on the flight schedule and how you feel about really early wake-up calls. Important: Even mid-July is not guaranteed to be beach weather in that part of Spain. San Sebastian averages 10 rainy days (over 5 inches of rain) in September. Most of the (few) people I saw in the water in June were wearing wetsuits. If you want beach/pool weather, you would be much better off staying in Catalunya, and Catalunya has a lot of interesting destinations beyond Barcelona.

If you want to see any of the following places in Barcelona, you should buy tickets in advance to avoid very long ticket lines and possible sell-outs. Only Camp Nou sells out really early, but individual time-slots at other sights may fill up. I think the first time period is perhaps the most popular, because the places are not crowded when you initially walk in. I would use the first time slot of each day for one of the problem places.

• La Sagrada Familia
• Parc Guell (no tickets sold at the park)
• Casa Mila/La Pedrera
• Casa Batllo
• Palau de la Musica Catalana (English tours sometimes sell out; you might be able to do a self-guided tour in September; I am not sure.)
• Picasso Museum (listed for completeness, though you said no museums)
• Camp Nou Soccer Experience (must be booked way in advance)

Include Parc Guell especially with a child. The lizard stairs are fun as are all the mosaics. Also, go to the beach in Barcelona even if just to have lunch in that setting.
Flamenco dancing is usually found in Andalusia, Sevilla. Barcelona is Catalan, different from “traditional Spanish” Spain. You have probably heard of the Separatist movement in Barcelona. Go to Mont Juic. Views, Olympic
sites, Musee Joan Miró.
Skip Monserrat. Use the time for Barcelona.
You could fly to Bilbao or Hondarribia( San Sebastian’s airport) but with such a short time why not visit the Costa Brava just north of Barcelona? I agree with acraven, too much time taken up with airports, flying with so few days available. Perhaps Mallorca would work better. Many travelers combine it with Barcelona.
Pick Pocketing? Having a map in hand to slam on a women’s arm as she slid her hand into my husband’s pocket on the Metro platform helped fend her off. She screamed and everyone ignored her. We were warned about pickpockets every single time we left our hotel and in some restaurants too which has never happened in all of our travels. Just be aware of your surroundings as in any city with crowds. Don’t hesitate to use the Metro.
And go out at night! Spain has very late hours and you’ll adjust.

You said that you plan to "be out for sunset/dinner as usual but usually not out very late." Here's a link to sunset times in Barcelona in September.

Now match that up with typical Spanish meal times. This is only one of many resources for when to eat what and where in Barcelona -- Spanish Mealtimes: Where to eat 6 times a day in Barcelona.