Good morning. I have messed around a bit and experimented with recording from a cassette tape deck into WavePad. You are likely aware of much of what I state here; I am just trying to find common ground to better discuss the process. I used a windows 7 machine with WavePad version 5.1. Sorry if I get too wordy ....
Looking at the specs of the Behringer UCA202 it looks like the only gain control it has is for the headphone out. So the crux of your situation (and probably the reason you posted to begin with - duh) seems to lie in setting levels in WavePad, and possibly other sound settings in your computer. Apologies in advance for not addressing that at the moment, I will look further into simulating your exact configuration after I locate some other hardware from the depths of my closet. The usb interface I am using has output level controls for each channel.
An alternative would be to connect the tape deck to a stereo/receiver, and connect the tape out to the Behringer, then you could control the output level with the receiver. That is actually the method I use to record (with Golden Records) from a phonograph, and from my cassette player.
As a test, I have the rca out from my tape deck going into a Lexicon Alpha, and the usb from that connected to my pc.
When you click the Record button (red circle) at the bottom left of the main window (where the other transport function buttons are located) the Record Control window will open.
Here you need to set the Recording > Device: using the drop-down pick your usb device. (I am also monitoring through the Alpha, so I chose it in the Playback > Device: drop-down.)
Clicking on the record button in the Record Control window initiates recording, and levels can be monitored via the Recording Volume display. A test would be required to set levels; but in answer to your first question in the op, levels while recording are displayed via a peak meter. You only see the waveform after the recording is finished and in the main window.
To finalize the recording (bring it into a file on the main WavePad window) you close the Record Control window (the X at the top right.) Now the waveform will display. Some trial and error may be required to get satisfactory levels set.
One thing I notice is that the Pause function isn’t active; you can only Stop the recording. After Stopping, if you start Record again you will lose the previous recording, so this seems to indicate that if you want to record multiple ‘takes’ you need to close the Record Control window after each ‘take’.
Another thing I noticed is that after closing the record window, the new recording will be placed at wherever point the cursor is positioned – no problem if it is a new WavePad session, or you have started a new file, but something to be aware of if you are recording multiple sessions into the same file.
This probably doesn't help you much, but thought I'd get all that out of my system. I'll get back later when I try something else.
Dan
edit to add: does you tape player have an output volume control?