I wanted to ask wether one is allowed to say, "Bismillahir-Rahmanir-Raheem" instead of "Bismillah" before performing ablution. I read that according to Ibn Taymiyah and other scholars that it is fine to say the whole word before eating, so I am wondering whether this is applicable to the ablution as well. May Allaah bless you.

All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger. 

It is permissible for you to say the whole Basmalah before performing ablution and before eating as well as before other matters for which it is permissible to say the Basmalah, but you should know that it is enough to say 'Bismillaah' to achieve the virtue of the Basmalah, as was stated in Al-Majmoo’ by an-Nawawi  “The Basmalah is desirable in ablution and all other acts of worship and other acts, even before having intercourse ... Al-Bukhari wrote a Chapter in his Saheeh which he entitled, Chapter of saying Basmalah in all conditions and before having intercourse ... and know that the perfect form of Basmalah is to say 'Bismillaahir-Rahmaanir-Raheem'; and if one only says, 'Bismillaah', then the virtue of the Basmalah has been achieved, and there is no difference of opinion among the scholars in this regard.”

What you mentioned about Ibn Taymiyyah regarding saying the complete Basmalah when eating is mentioned in his Fataawa as well as in other books, but he did say that saying the complete form of Basmalah when slaughtering is not suitable.

He said in Majmoo’ Al-Fataawa, “If one, when eating, says, 'Bismillaahir-Rahmaanir-Raheem', then this is good as he completed the whole formula of the Basmalah, contrarily to when slaughtering, as it was said that it is not appropriate to say the entire formula when slaughtering.”

Allaah knows best.