Someone told him that it was not obligatory to wash the arms in wudoo’; what is the ruling on the prayers he offered previously?

Firstly: 

Washing the arms is one of the obligatory parts of wudoo’,
without which it is not complete. That is proven by the Qur’an and Sunnah,
and by scholarly consensus. 

An-Nawawi (may Allah have mercy on him) said: Washing the
arms is obligatory according to the Qur’an and Sunnah, and (scholarly)
consensus.

End quote from al-Majmoo‘, 1/418 

Ibn Qudaamah (may Allah have mercy on him) said: With regard
to washing the arms up to and including the elbows there is no difference of
opinion among the scholars of the ummah that it is obligatory to wash the
arms when doing wudoo’. Allah, may He be exalted, stated that in the verse
(interpretation of the meaning): “wash your faces and your hands
(forearms) up to the elbows” [al-Maa’idah 5:6].

End quote from al-Mughni, 1/85 

The one who told you that is either ignorant and does not
know the simplest thing about Islam or you did not understand what he said
properly. 

In that case what you must do is learn from this an important
lesson in life: that you should not ask anyone about your religion except
one who is known to be knowledgeable; you should not ask the first one you
meet or learn your religion from anyone who speaks about it, even if they do
so without knowledge. 

Moreover, you should pay proper attention to what is said to
you, so that you will understand it correctly. 

For information on the seriousness of fatwas given without
knowledge, please see the answers to questions no.
21018 and
126198. 

Secondly: 

If a person omitted one of the conditions, essential parts or
obligatory parts of an act of worship because he was unaware of what was
required of him, then he is excused because of his ignorance and there is no
sin on him for what he did out of ignorance. He is also not to be instructed
to repeat the prayers and so on in which he made mistakes.

Based on that, if a person did wudoo’ and did not wash his
arms or any of the parts that must be washed in wudoo’, he has to repeat the
prayers that he offered, because he did not do wudoo’ as enjoined by Allah,
unless he was unaware of the ruling, in which case he does not have to
repeat them, especially when there are so many prayers. But what the Muslim
must do in the future when he does not know about some matter of his
religion is ask someone whose religious commitment and knowledge he trusts,
so that he may do what Allah has commanded him to do with proper knowledge
and insight. 

See the answers to questions no.
21805 and
45648 

Secondly: 

With regard to rinsing the mouth and nose in wudoo’, there is
a significant difference of opinion among the scholars. The majority of
scholars are of the view that it is not obligatory to rinse the mouth and
nose in wudoo’. 

The view on which the fatwas on our website are based is that
both actions are obligatory in wudoo’. 

This has been discussed in the answer to question no.
153791 

But if you consulted some scholars who issued a fatwa saying
that it is not obligatory, there is no blame on you for that; therefore one
is not required to make up any of the prayers that one offered without
rinsing the mouth and nose. 

And Allah knows best.