Yes, being aware of the apparent symptoms would be very helpful. I believe it could be nice and immersive if you could get it in the same fashion as you do with the current hunger and thirst messages in the chat for any kind of symptoms you get. But you should also be able to look them up at demand.

Maybe you could have a dedicated diagnosis action that would let you diagnose yourself and other players. That could be a lot of fun.

I can confirm this. Using the alcohol to clean your wounds (or taking antibiotic pills) seems to update your infection status (or perhaps it just sets it to stage 4 and stage 1-3 is invisible with no messages?) and you have to wait for the wounds to be cured.

After some time the wounds will become totally clean and you become healthy, or you might have to clean your wounds again. I'm a little unsure if using the alcohol tincture/antibiotic pills once are supposed to clear the infection completely and the status isn't updating to healthy/healing or if you sometimes actually have to use it a couple of times for it to heal you fully. Re-logging might update your status correctly to healthy, I haven't been able to test that yet.

Blood regeneration is working. If you eat and drink until your stomach is full and you're still not regenerating, it most probably is because your wounds are infected (every time a zombie hits you it has 20% chance to infect you), but the "sick" status isn't showing up.

Cleaning your wounds with alcohol and/or taking some antibiotic pills will update your status and show "sick" and give you a message that your wounds look cleaner and they hurt less. Now wait for the sickness to be over, and you will be regenerating/healing. If you don't notice a change in color/clearness in 5-10 minutes you might need to eat/drink or clean your wounds again.

Also Vitamins might or might not speed up the progress.

Refer to this site on how much you need to eat/drink and the different statuses. I'm not sure how accurate it is, but it helped me.
http://dayzdb.com/guide/11-standalone-status-effects

Here's some screenshots I took.

http://imgur.com/a/3DDO1

In the second image you can see the texture it appears to be a problem with in this case.

Here are my game settings:
http://pastebin.com/rAt6BdYx

My computer specifications are as follows:
Windows 8.1 Pro 64-bit
Intel Core 2 Duo E6850
ATI Radeon HD 4800
8 GB RAM DDR2