If I open spam coming through my eMail, does the spammer see my eMail
address so that he can keep it active? If I visit a website, does that
website have my eMail address so he can spam me later?

Greetings!
The short answer to your questions is yes, opening a spam message or
going to the website advertised can cause you to receive even more
spam.

"Just delete it.

Don't try, don't buy, and don't reply. Never visit Web sites or buy
anything advertised in a spam message. Spam is almost always a scam.
Just delete it.

Don't respond.

Never open, reply to or click on the "remove" or "unsubscribe" link in
a spam message. These actions can confirm your email address, causing
you to receive more spam."

http://www.stopspamhere.ca/#2

The reason this happens is based on a couple of tricks the spammers
can pull.  In today's technological environment, almost all email
supports html.  This means that spammers can put pictures and other
things into the messages that they sent you.  A very simple way for
them to see that you opened the message would be to embed a picture
tag, such as...

<img scr="http://www.randomspammer.com/2432fa2.jpg"> 

in your email.  When you load the message it pulls the picture down
from the spammers server.  Each picture id would be a unique end
number specific and logged to your email address.  When the server
logs show that picture 2432fa2.jpg was pulled down they know that you
must have opened their email and thus your address is active.

When following a link to their website they'll use a similar trick. 
The link for you to click on would be something like...

http://www.randomspamer.com/index.php?id=234234 

The id 234234 would be unique to your address and would tell them that
not only did you open the message, you followed the link and thus are
receptive to email advertisements. A trick they have been doing for
awhile as well concerns those "Click to unsubscribe me" type things on
unsolicited emails.  When you click to have your email taken off the
list they know they found an active one.

Best of luck!
djbaker-ga

Search Strategy:
open spam verify email go to website
://www.google.com/search?hl=en&lr=&client=safari&rls=en-us&q=open+spam+verify+email+go+to+website&btnG=Search

"Opening spam can often alert spammers that they have reached a
working email address and potentially sell your email address to other
spammers. If you do not know the sender and the subject line has odd
characters we suggest that you do not open the email but to delete the
email."

http://www.gwu.edu/~virtual/mailfilter/spam.html

I hope this helps with the first part of your question.

Have a good day.

I feel it's not necessary to be quite so paranoid. Merely displaying
the plaintext of a message can't send any information back to the
sender, and you can configure your email client so that it does
nothing more.

If your email client is set to display plain text only (no images, no
JavaScript, no HTML), and to refuse to respond to "Received" or "Read"
receipt requests, then you can safely view spam.

Alternatively, if you don't want to do this (e.g. because you want to
see images in your emails) most email clients allow you to view the
message source. This is just plain text and does not send information
back to the sender. You will have to scroll past the headers to see
the message proper. This can be quite revealing, e.g. for a spam
message you will often see that the hyperlinks go to different places
from what the text suggests. Then, you can delete the spam without
being tempted to open it in the usual way.