Let's see if I can nail down all your issues.
1) She cannot check in until about 4AM. Even online checkin will not give a BP
2) She will get lounge access (TG C,D and/or E concourse) but I don't know what time SQ in B concourse opens
3) TG has showers in the C and E concourse lounges
4) TG lounges open at 5:15AM so it's very possible she will have BP, clear immigration and get inside the terminal only to find that the lounges are not yet open.