I have some questions to ask about Hydra System AmigaNet 500: http://amiga.resource.cx/photos/amiganet500,2. Is this a normal Ethernet standard card like you see in normal nowadays PC? Can I just hook it directly to my modem and I immediately get access to the internet?
The short answer is "no". The "Hydra System AmigaNet 500" was designed and built 25 years ago, and the limitations of its design will restrict you to using the Internet, if at all, to how this was done back in 1990. No web browser, no gmail...
To begin with, you need an Amiga 500 to plug this hardware into. If I remember correctly, the Hydra Systems network driver software had issues with Kickstart 2.0, which is troublesome because the driver is not provided on a floppy disk, but it is stored in the ROM and cannot be changed or replaced. Chances are that it will not work well with contemporary Amiga network software.
The next problem would be in how to connect your local network and your modem (assuming that it is a cable modem or DSL modem) to this device. Modern Ethernet hardware uses a different kind of connector than you will find on the "Hydra System AmigaNet 500". The specifications state that it has an AUI interface and two BNC connectors, which means that you will have to find an additional set of hardware which connects a modern Ethernet network to the "AmigaNet 500". This is not impossible, but it's likely that you will have a hard time finding the 20 year old hardware to make this happen and which is still in good working order.
Put another way, trying to use the Amiga 500 combined with the "Hydra System AmigaNet 500" is like trying to make a 19th century narrow gauge steam locomotive run on the modern European high speed train network.
I am not so sure I understand the speed of it. Can I download 1 MB/sec file? How about 512 KB/sec file? Can I do that?
If I remember correctly, tests with an Amiga 600HD suggest that you may not get much more than 140 KBytes/second out of this type of hardware configuration. Hypothetically, an Amiga 500 with a "Hydra System AmigaNet 500" could probably reach that, too, but it's not a given.
There is works on a new internal accelerator for the Amiga 500 that suppose to give the Amiga 500 a major boost in CPU speed which outshines all the normal accelerators for the A500 (which when I look at them is truly horrible). Would I get a good internet performance or would I drop to 1 byte/sec even with this card? I understand zorro 2 is a horrible expansion port because it can only do 3.5 Mb/sec. However, this is great speed for internet for the A500 and I will be really happy if I get half or even 1 Mb/sec speed.
No, this won't work. Increasing the processing speed of the machine has little impact on how fast the network traffic is being processed. The limiting factor is the speed of your system memory. There is not a lot to be gained by trying to upgrade it.
Everything considered, I would strongly warn against sinking money into this hardware configuration if you expect to use it on today's Internet and not be thoroughly disappointed.
Given that the networking hardware has its limitations, the quality of the network drivers and the required additional investments into making the Ethernet connection work with today's technology, this has red flags all over it...
