The permitted material differs across juristic views but must be pure. Intention is obligatory for tayammum; it is recommended for wudu under the Hanafi framework.
Ordinary nullifiers of wudu and regained access to usable water nullify tayammum. One tayammum may cover multiple prayers under the Hanafi view while it remains valid.
Special rules for funeral and Eid cannot simply be transferred to Jumu‘ah or routine time pressure. The search for water and asking for it are governed by reasonable probability and actual accessibility.