May I use on Shabbat an hourglass with lines showing how much time passes? And can I use a sand timer which has no lines but a fixed time such as two or three minutes?

One should not use an hourglass with lines on Shabbat, unless it is for the purpose of a Mitzvah. It is Muktzeh and should not be moved in accordance with the law of Keli Shemelachto L'Issur (a utensil designated for prohibited use) unless it's for the purpose of using the object itself for a different, permissible use (Tzorech Gufo) or for the space it occupies (Tzorech Mekomo).(שלחן ערוך או"ח סימן שח סעיף נא ומ"ב ס"ק קסה). Regarding a sand timer which has no lines but a fixed time such as two or three minutes, one who is lenient and uses it on Shabbat has whom to rely on, and one who is stringent and refrains will be blessed. (פרמ"ג או"ח סימן רנב במשבצות זהב ס"ק ז, לבוש סימן שח סעיף נא, והובא גם בכף החיים אות רסט וע"ע באות רעג).