Yes, those are both Rome, Italy. The Coliseum and the Arch of Constantine.
I know how tempting it is to try to go EVERYWHERE, but it's usually not a good idea. It would be like someone planning a trip to the US and thinking they could visit NYC, Washington DC, WDW, and perhaps one of the major national parks out west, all in a week. You just can't. Well, not and enjoy it
Yes, airports are time-consuming. More than you would think. I'll head over to your Paris thread in a bit and tell you more about what we did there. (I have a cake in the oven right now - lol)
Okay, London. First know that I *love* London; I spent a semester abroad there my junior year of college and still didn't see everything. I went back for 3 weeks when I was 23 and still didn't see everything. I took my family there is '06 and we were there for 9 days, and I felt we barely scratched the surface. But...yes, it can be done as a day trip from Paris. You will just have to pick the things that are MOST important to you. They will not be the same things that are important to me, or to anyone else. Decide what YOU want to see. You will leave early and get back late, but it's do-able.
The Eurostar is very nice and travels at nearly 200mph, so it's about 2 hours to Paris. I think you need to be at the train station 2 hours before departure, but it's easy to get to on the Metro, and it's centrally located in Paris. You need all that time because, unlike with planes, you go through customs and immigration before you board. This means you are legally in the UK when you board the train, and when you arrive in London, you can just...walk away. Awesome.
What I would recommend is flying into Paris and out of London (or the other way around), taking the Eurostar between them one way. A ticket can be as cheap as $60 if you book in advance. Then you can have more than one day in London. You could maybe do 4/3 or even 5/2 depending on how much you want to do in Paris. But, yes, you could EASILY fill 7 days in Paris without even a day trip to the countryside. You might want to consider something like a day trip out to Normandy (if that would interest you) or even down to Nice. Just to see something of France besides Paris.
The downside of not doing London as a day-trip would be having to take all your stuff with you and check into a hotel there. With a day-trip, you would need only your camera, passport, money, etc.
Or...you can get to Amsterdam on the Eurostar in only 1 hour, if you'd like to see canals without going to Venice, and eat wonderful cheese, see Anne Frank's house, and see Dutch masterpieces in the Rijksmuseum. Just a thought.

And Brugges is only an hour from Amsterdam, and it's one of my favorite cities in Europe...oooh, I'll stop now. See how easy it is to want to go just one more place! I even wanted to add Brugges onto our trip, but it would have meant cutting a day off Paris, so at some point, you just have to remember that Europe has been there for a LONG time, and it will still be there later, waiting for you.
In a daytrip to London, I would suggest taking one of the Open Bus tours, as you would see the whole city in a couple of hours, with a nice commentary, and then go back to what interests you, whether that's Westminster Abbey, St. Paul's Cathedral, the British Museum (the Rosetta Stone! I was in awe to see it in person!), or taking in a matinee on the West End. Unless you're there when the Queen is not, you can't visit Buckingham Palace, but you can tour Kensington Palace, which is where Queen Victoria was born, and where Diana lived. There is a tea room on the grounds, where you can eat even if you don't want to tour the palace. A ride on the London Eye is amazing, and you could squeeze in a visit to the TOwer of London to see the Crown jewels and the Bloody Tower, if you wish.
Lots and lots to think about! The forums at trip advisor are a treasure trove of help as well.

Have fun planning!