(I'm a native Chinese speaker from Mainland China. People from other Chinese-speaking regions or countries may feel different from me.)
雖然 x 但是 y
sounds fine to me for all your examples.
However, to me the turn embedded in 儘管 x 但是 y
sounds a little bit stronger than that in 雖然 x 但是 y
. That's why when the conditions are very extreme, 儘管 x 但是 y
sounds more natural to me.
I think neither 即使 x 還是 y
nor 即使 x 仍然 y
is appropriate for your examples.
A critical difference between a. 儘管 x 但是 y
, 雖然 x 但是 y
and b. 即使 x 還是 y
, 即使 x 仍然 y
:
For group a, x is a statement that the speaker believes to be true, while for group b, x is only a supposition (usually an extreme one).
e.g.
儘管我們安裝了最好的安防系統,賊還是進來了。
→ The speaker believes that the system has been installed and some
thief or thieves have found a way inside.
即使我們安裝了最好的安防系統,賊還是會進來的。
→ The speaker makes a supposition that (EVEN IF) we installed the best
security system, and he shows that he believes that still some thief
or thieves will find a way inside.
Since for group b, x is only a supposition, the sentence below will sound weird:
即使我們安裝了最好的安防系統,賊還是進來了。
→ The speaker makes a supposition that (EVEN IF) we installed the
best security system, and he shows that he believes that some thief or
thieves have already found a way inside.