Hi Axx...

many of the problems you describe sound to me like you are using the wrong Java version. Phex needs at least Java 1.3. Please check it with "java -version". Which system do you use?
That should solve Problem #1, #2, #4
I don't have any other explanation for these problems.

#3
That means you have 0 currently running download and 3 download in total.

#5
You only need to do that if you have a proxy or want a other IP shown to the public. Just leave the field empty will fit for most users.

#6
Yes it's time to live. It means how many hops a message go through the net. A value should not be over 10 at max. Many clients drop to high ttl's a TTL of 5-6 is often enough.

#7
A passive search analyzes the searches that go trough your client. It's not consuming bandwith only CPU. But it will biring much fewer results. It is usefull for a long time search. Let it run over night to find sharing hosts.