Is the Umrah valid if ablution (wudu') was performed quickly in an open area with doubt as to whether water reached all parts of the body, and what are the consequences if it is not valid?

If you doubt the validity of your purification after completing ablution, this doubt is disregarded, and your ablution and circumambulation are valid. However, if the doubt occurred during ablution, it is obligatory to complete the purification correctly; otherwise, the ablution is invalid.

Accordingly, your 'Umrah (definition) is invalid, and you must refrain from the prohibitions of Ihrām, return to Makkah to complete the circumambulation (Tawāf) and the ritual running (Sa'ī), and then exit the state of Ihrām (Tahalul). This is the view of the majority of scholars.

However, you may adopt the view of Sheikh al-Islam Ibn Taymiyyah, who held that purification for Tawāf is a Sunnah (definition) and not an obligation. Based on this, your 'Umrah and your exit from Ihrām are valid, and there is nothing upon you. This is not considered blameworthy leniency.