How do I check the health of my 3ware RAID array under any Linux distribution? How do I access 3ware RAID Array web interface?

You need to download required command line tools from 3ware support web site. You can also find the same on driver cd / floppy disk. For example, I’ve downloaded a file called tw_cli-linux-x86_64-9.4.1.3.tgz for my 64 bit Linux server from above site. You need to get tool according to your device.
# tar -xvf tw_cli-linux-x86_64-9.4.1.3.tgz
Once tool is installed look for command called tw_cli. It is a Command Line Interface Storage Management Software for AMCC/3ware ATA RAID Controller(s). It provides controller, logical unit and drive management

To see the health of the RAID array, enter:
# ./tw_cli /c0 show
# ./tw_cli /c1 show
Sample output:

Unit  UnitType  Status         %RCmpl  %V/I/M  Stripe  Size(GB)  Cache  AVrfy
------------------------------------------------------------------------------
u0    RAID-1    OK             -       -       -       232.82    ON     ON     

Port   Status           Unit   Size        Blocks        Serial
---------------------------------------------------------------
p0     OK               u0     232.88 GB   488397168     WD-WCAV20957520     
p1     OK               u0     232.88 GB   488397168     WD-WCAV20957786     

You can read more about command syntax here or just refer to local man page called tw_cli. I don’t recommend browser interface over Internet it can create a security risk.