Since this year Tisha Be’Av is Nidche until the 10th, when would be the earliest opportunity to launder clothes and to trim one’s hair?
Also, at one point during the day (Tisha Be’Av) is one (normatively) permitted to put on Tallis and Tefillin?
Haircuts and laundry may be done immediately after the fast on Sunday night. There is however a custom to refrain from meat and wine the night after the fast being that it is the night following the fast.
see Mishna Brura 558:5.
Tallis and Tefillin are put on for Tefillas MIncha.
see Shulchan Aruch 555:1.