Is it permissible to recite the Quran without wudu, and is it valid to perform tayammum for that, especially with the difficulty of maintaining wudu for a long time?

The ruling on reading the Quran without ablution has been detailed in a previous answer. As for tayammum (dry ablution), it is not a substitute for wudu' (ablution) if wudu' is obligatory. However, in cases where wudu' is not obligatory, such as reciting from memory, some scholars have permitted tayammum as a recommendable act, drawing an analogy to the Prophet’s tayammum for returning a greeting.