What is the ruling on someone who doubted the invalidity of their prayer, then remembered its validity after intending to repeat it? And is it permissible to suffice with washing some parts of the wudu' twice and others three times in order to catch the congregational prayer?

There is no consideration for doubt that occurs after the completion of the prayer, and therefore, it is not obligatory to repeat it. If you have entered into prayer, you may conclude it after two rak'ahs with the intention of performing a supererogatory (nafila) prayer. Triple washing during ablution (wudu) is recommended, and it is permissible to wash a limb twice or even once. However, leaving the triple washing may be requested as a recommendation (nadban) when there is a fear of missing a congregational prayer for which no other is expected, or as an obligation (wujuban) when time is short.