Hi, and welcome.
Here's a few suggestions to some of your questions, which by the way not belong to the Support section of this board.
First of all: Facets documentation.
(2) The only thing that changes when using my Facets plugin is Library selection - and it displays whatever's playing now (which I believe should be in Library selection (playing)?). All of the other playlists seem random to me. How do I see the contents of an album without playing it (like in Winamp)?
In Facets' toolbar be sure the drop-down list is set to Library.
In Facets' preferences in the Library part set 'Selection action:' to None. See screenshot.
4. How do I only see the albums that are rated 5 stars? Once I click on Filter > Top Rated, it shows nothing (even though several albums are rated 5 stars)
You already have the Playback Statistics (PS) component installed. It also handles ratings, but the component uses it's own database; it doesn't read|write these metadata from|to the audio files. When you install the component, it's literally day 0. I don't know how Winamp handles and formats ratings, but if they are kept in a tag, for example named rating, you might have luck with this:
$meta(rating) IS 5
as a Facets filter for the highest rating. See also: Playback Statistics, Common sources of confusion.
The PS component is able to import (rating) data in XML format. But even if Winamp has XML export functions (via an add-on maybe) this will probably be of no use. Internally PS uses these proprietary values for ratings 1-5:
<PlaybackStatistics Version="3.0" Mapping="C653739F-14B3-4EF2-819B-A3E2883230AE">
<Entry ID="aee1a66f1378eb4f" Rating="63" />
<Entry ID="acc3139f8873aeb9" Rating="106" />
<Entry ID="8a18fa9adcbe9bad" Rating="149" />
<Entry ID="16b2f3ec89bd5823" Rating="191" />
<Entry ID="b09bb29137bd4b80" Rating="234" />
</PlaybackStatistics>
6. How do I make columns' contents not case-sensitive, like in Winamp? E.g If I'd like to merge 'Alternative rap' with 'Alternative Rap' without actually changing the tags?
$caps(%genre%)
'AlterNative rap' -> 'Alternative Rap'
$caps2(%genre%)
'AlterNative rap' -> 'AlterNative Rap'
$lower(%genre%)
'AlterNative rap' -> 'alternative rap'
$upper(%genre%)
'AlterNative rap' -> 'ALTERNATIVE RAP'
See Titleformat Reference string functions.
7. If the album has no title, can I still make it appear in the Album section as, for example, "(no title)"? Right now it displays nothing in such situations.
Try
$if2(%album%,'('no title')')
being the same but shorter than
$if(%album%,%album%,'('no title')')
See Titleformat Reference control flow functions and Facets doc on Missing fields.
Good luck with the transition from Winamp to foobar2000.
Addendum
If Winamp saves rating values in a metadata field, it's not named rating. From Facets' documentation:
Checks playback statistics %rating% first, then metadata field rating.