1. Airfare: It's worth it to get a points credit card and do a referral to max the points. Some cards will waive the annual fee for the first year, and then you can cancel the card once you reach the obligatory spend amount to get the points. You have a lot of time to plan. Though we are booking from Canada and YMMV, I find that the European airlines have great seat sales at the end of August and early September. The last few years, we booked during the August seat sale, only to find out that the prices are even lower once September comes. Sign up to the airline newsletters for alerts. We love Air France. The food is soooo much better than any other airline, even in economy. When we book during a seat sale, we pay about 800 Canadian per ticket. Sometimes less. As suggested, best to book return to one city, then easyjet or ryanair for a London-Paris return. Or try the Eurostar. Do be mindful of the airports. It's not only a huge pain to change from Charles-de-Gaulle to Orly, or Heathrow to Gatwick, it also costs $.
2. AirBnB, definitely, and there's also VRBO, HomeAway and other sites. Hotel staff ... pfft. Just do some research on the interweb and you'll be fine. Make sure you get a washer in your AirBnB, and that way you can wash as you go, and pack a whole lot lighter. We go for 6 weeks each year and we only bring carry-on. Dryers are rare, so don't expect one. Just hang your clothes to dry; most places provide the racks, but you don't want to be washing the night before your departure. Count on needing a full day for things to dry.
3. Paris: It's tough to find an open restaurant in Paris on a Sunday night, and Mondays aren't the greatest either. Versailles ... ugh. You couldn't pay me to go there. Loads of big stinking tourist buses outside, long lines, full trains. I had fond memories of visiting it once back in 2002 when I lived in Paris, and had friends who lived nearby, so we went back in 2013 and we were appalled. You CAN have a bad meal in Paris, so do your research. I recommend the Rodin Museum, but just do the garden for 5 Euros, not the interior. The garden is where all his most famous sculptures (e.g., the Thinker) are located, and the gardens themselves are beautiful. And please, please learn a few french words: S'il vous plait (please), merci (thank you), and ALWAYS say bonjour (or bonsoir depending on the time) when you walk into a restaurant, store, or anywhere else.
London: You probably won't have the same issue re. Sundays/Mondays in London, but it depends what you want to see and do. We loved the British Museum. If I recall, most museums in London are free (though donations are appreciated). Not sure if that's changed. Food-wise, London has improved dramatically in the last 20 years.
4. Saving on food: In both cities, the supermarkets are great, and so are the bakeries. In London, there's a chain called "Pret a Manger" that sells healthy, prepared, takeaway. Also, there are lots of Indian restaurants for takeaway. In Paris, you might like the Asian takeaway places, or the fallafel joints (such as l'As du Fallafel).
5. Paris: A cruise along the Seine, one really great meal (e.g. at a place like Au Trou Gascon in the 12th), and a walk through the Jardin des Plantes in the 5th (free!). Or the Rodin Museum gardens if one of those is not to your taste.
London: The British Museum, a walk down The Mall, and a stroll through Covent Gardens. Hyde Park is also nice.