RE 7 yes. Dark Souls 3 no. Dark Souls 3 requires a good CPU for all those physics and animations. That said maybe From is working on it and if Dark Souls Remastered is a success on the Switch they'll bring Dark Souls 2 SOTFS and Dark Souls 3.
Yes the third party support was very good. No different than 2k17.
Switch has a weaker CPU than PS3 and in portable mode I've heard that its GPU is less powerful than a PS3. It has more ram and a more modern architecture but I don't think that would be enough.
Look at Doom say. It runs at 1080p60fps on PS4 at medium to high settings. It runs at 640p30fps on Switch docked with lower than low settings. That with a very scalable and good engine like Idtech6. Unreal engine 4 games struggle to even run at 30fps at 1080p on PS4, it would get real bad on Switch. There is only so much downgrading possible before the game loses its soul. Those Wii ports of PS3 games felt nothing like the PS3 version. I don't think that is an ideal experience for a Switch owner whose spending $60 on a game.
The CPU part is not even close to the truth. The A57 (out-of-order executions support, 4 cores, 2 MB shared L2 cache, faster cache system) is the Switch is miles ahead of the PPE (in-order design, single core 2 threads, 512KB L2 cache, slower cache system compared to A57) in the PS3. As for the SPEs, it is true that they would be better at highly parallel SIMD tasks than the Neon units in the A57 (heck they are slightly better than the SIMD in the Jaguar cores in certain situations) but those functions are now largely in the GPGPU at much faster speeds than they would ever run on a regular CPU or SPEs. I recall early in the PS4 and Xbox One's life people saying how the Jaguar would be slower than the chips in PS3 and Xbox 360 because those chips ran at higher clock frequencies, and in practice the Jaguar completely trashed those chips.
As for the GPU, I am assuming you are looking at the floating point operations per second (FLOPS), in which case yes the PS3 is theoretically faster than the Switch in portable mode. However, that number may be deceiving because there are many other factors that need to be taken into account, and in practice the Switch in portable mode should be, at worst, on-par or, most likely, even faster than the PS3 GPU. Here is a good example as to why GFLOPS are not the end-all, especially in gaming performance. This link (https://www.tweaktown.com/tweakipedia/116/fury-vs-gtx-1070-battlefield-dx11-dx12/index.html) benchmarks the AMD Radeon Fury X (8601 GFLOPS) compared to an Nvidia GTX 1070 (5783-6463). Going by the GFLOPS alone, the Fury X should be able to handedly beat the GTX 1070, but in most cases the 1070 outperforms the Fury X. Now it should be noted that Fury X and GTX 1070 were released in 10 month period from one another; there is a 10 year gap between the Maxwell-based GPU in the Switch's X1 and the PS3's GeForce 7-based GPU, so even while the theoretical floating point is slightly higher on the PS3 than Switch in portable, there are numerous other advantages that the Maxwell GPU has over its PS3 predecessor that should give Switch in portable mode the performance advantage (even if it is a narrow advantage).