1) Saying Tehillim on Tishe Beav
May one say Tehillim on Tishe Beav?
Erev Tishe Beav: Yes, even past midday.
Tishe Beav night from sunset: No.
Tishe Beav day until Chatzos: No.
Tishe Beav after Chatzos: Yes. One may say Tehillim by Mincha time and so is the ancient custom.
For sick person: One may say Tehillim for the sake of a sick person at any time.
Sources: See M”A 554:6; M”B 554:7; Aruch Hashulchan 554:6; Kaf Hachaim 554:20; Divrei Malkiel 6:9 ; Nitei Gavriel 50:8; 75:22; Piskeiy Teshuvos 554:4
2) Must one sit for the recital of Kinos or may he stand?
There is no requirement to sit on the ground while saying Kinos, and the main thing is not to sit on a regular bench or chair. However, if one desires to stand while he recites it then he may do so, and so is in fact recorded in the original source in which the recital of Kinos is mentioned, that they would stand and recite it.
3) Doing laundry before midday of the 10th if traveling:
If one is traveling after Tisha B’av and needs to do laundry, may he be lenient to do so before midday of the tenth?
 See Michaber 559:3 [we sit in Shul on the ground until Mincha]; Taz 559:4 “In truth if one desires to stand he may certainly do so, as there certainly no obligation that one specifically sit and to sit on the ground.”; Miseches Sofrim 18:5, brought in Tur 559:3 and Ramban Toras Hadam p. 98, Beis Yosef 559, Orchos Chaim 1:17, Haguda Sofrim 16, Machzor Vitri 527, “after the Torah reading one stands and dirties himself with earth, and messes up his clothing and reads [the Kinos] with a cry and moan.”; Nitei Gavriel 61:1 [writes to sit and say-but no source]
 Piskeiy Teshuvos 558:2 based on ruling of Mamar Mordechai that the prohibition only applies to meat and wine, and in a time of great need one may rely on their opinion.
 See M”A 558:1; P”M 558 A”A 1; M”B ibid; Kaf Hachaim 558:6; Orchos Chaim 558:1