Sounds like you're off to a good start, I'm a fan of the stock GM HEI distributer as a replacement to the points fired dizzy, they are super dependable and easy to come by at low cost.
Note that both big and small blocks take the same dizzy so you can drop one right in from a garden variety 350.

 

i found that prices vary. does it matter which brand/manufacturer?
For example found this one for around $490 https://www.gmperformancemotor.com/p...GD-e0Yw0r3yQw6

while Classic Industries very similar is $195 https://www.classicindustries.com/pr...E&gclsrc=aw.ds

I also had a question about this part connected to the fuel pump. (attached below), is it related to fuel pressure?

 

I don't know that I'd buy either of those, the one seems pretty expensive the other is probably made of Chinesium.
I'd probably hit up a local parts recycler and try to pick up a used original GM one and treat it to a new cap coil and rotor.
I see stock HEIs on Facebook marketplace for around $100, with a little shopping around I'd be you can come up with one for $50 or less.
The one in my '78 pickup with a 454 has been flawless for a long time. I think I replaced the cap and rotor once in the last 25 years and that old beast always fires right up.
Not sure on the fuel thing but it looks like maybe a pressure regulator for an electric fuel pump.

 

I found some good ones on eBay.

 

I have another question, since i need to work on the distributor (changing lead wire and springs), is it okay to keep it plugged in and work on it?
Since I turned the engine by hand, do I need to adjust the timing once I am done working on the distributor?

 

The timing is mechanical. As long as you do not remove the distributer you should not have to mess with the base timing. You can strip it all the way down and not have to remove it unless you want to install new bushing or a new gear. Now after saying that if you are changing the advance springs that hook to the weights under the rotor cap you should check your total timing and the timing throughout the RPM range just to make sure it is what you want. That spring tension controls the timing advance. A manufacture may say a spring is stock but springs are touchy.

Also the reason timing is adjustable is to make up for wear in the ends. Timing will change as parts wear from the chain stretching and wear on the gears themselves and for fuel mixture. Rich likes a little more timing advance and if it is lean you want to sneak up on the timing and make sure you do not get spark knock. If you have a motor with an unknown history its best to check the timing. I suggest setting it back to stock until you are sure everything is fine and you can advance it to tweak a little more power out of it.

 

Hello. Sorry, i completely missed your last update. Thank you for the detailed explanation.