I can partially answer your questions :

1 : Yes, you will mostly see a good increment on Intel Cpu's since they both have increased IPC and to some extent better "speed" than Amd Cpu's , but basically you will want a pretty new ( I5 or I7) from last year with a high speed ( Above 3000 Mhz ). What is important to understand here is that even though AMD cpu's might seem faster Mhz wise they are ( looking away from upcoming Zen Cpu's ) not faster than Intel Cpu's, even sometimes when they have 2x speed than an intel they are still slower in games like Dwarf Fortress.

2 : No and Yes. Right now it seems DF are able to generate pretty big worlds , if you have to little memory they will start using HD swap and thus you can keep it going for a while longer though the game starts getting pretty slow , with more Ram it will take longer before this issue comes up. I've done a few tests by modifying the init files a little bit and while it's fun generating a world with "huge amounts of civs" it gets really slow fast. So that's where your cpu is mostly the limitating factos and by large your Ram speed and size. My best experiment with 64 bit DF got me to spend around 9 Gb of ram with a world that was around 1500 years old I think and had a everything maxed out...
Again if you have intel with at least Dual Channel memory try to see if you can have at least 16Gigs to 32 of at least 2400 Mhz speed with good timings.

3 : Right now I havent had a lot of problems with 64 bit at all while 32 bit have often crashed due to memory limitations and such. There are probably a few bugs but hopefully Toady will get the worst of them over time.

Has DF been capable of doing more/work faster in the last years because of the technological advancement? I am asking because I honestly can't see any difference in FPS.

Yes, but the number of features has also increased. Computers have gotten better but the load on computers from simulating everything has matched that.

Hoo boy, PTWing this.

I always wondered this myself too.

 Not only if advancements is gonna make DF faster, but if is gonna help the game handle things more effectively and help adding some awesome depth in gameplay , and making easily to Toady to add features, make the games feels even more alive(if this is possible)

 advances in the AI and improved dialogues, and help in general at all in the Super Epic History Generator/Fantasy World Sandbox Ultimate Game thing!!!

There are several websites dedicated to benchmarking CPUs and collating the results into nice lists. Like this.
Benchmarking tools run the CPU through some synthetic tests and then blurt out a number. They show how powerful a CPU is in general, but for specific use-cases, a CPU with a lower score can be better.

Normally, you optimize toward a particular goal.
If your goal is to make DF run faster, you should first define a set of reliable, real-world benchmarks, then running those benchmarks on different configurations of your system (hardware + software).
If FPS is the number you want to optimize, then at the end of benchmarking you will choose the configuration that produced the largest FPS number on average.

I've seen some talks around the forums of people wanting to set up a benchmarking framework so players could try it out on their machines and post the results. But I'm guessing this hasn't happened yet because the results wouldn't be surprising.

In theory the biggest bottlekneck on DF right now is your processor cache and And raw Ghz. In theory increasing the L3 cache size will increase performance but I am wondering since L1 and L2 caches have not been increased in I think decades if they are the new bottlekneck

I'd just like to note that the complexity and resonsiveness of DF have both signficantly increased since I first started with DF (and I wasn't even here at the start).  Sometimes not necessarily to my own satisfaction ("woah! My dwarves are now running around too fast for me to keep an eye on them!" "bogeymen, werecreatures and vampires..? Wtf?"  "Things can fly/climb over my walls now?), at least until I got used to them. And often 'improvements' were as a part of (or indeed actually were) optimisations/better handlings made in the code, even with the same hardware.

Anyway, we all know that quantum effects are the eventual target resolution, so welcome to the ride.  See you on the other side of the Singularity...