Tuesday is the day of the week between Monday and Wednesday.
We don't have any authentic evidence against wearing new clothes on a Tuesday. Some cultures can claim that but it is a matter of their own culture and not a matter if an Islamic teaching. There is a narration from Abu Hurairah claiming that Allah created the Disliked المكروه on Tuesday. This narration is in Saheeh Muslim ( Hadeeth number 2789) and Musnad Ahmad ibn Hanbal 2/327 and Al-Bayhaqi in al-Sunan Al-Khubra v.3, p. 9 and Tafseer Al-Tabari , v.21, p. 433 and other Sunni books. This narration has no value according to Ahlul Bayt (AS). Even many Sunni scholars like al- Bukhari and Yahya Ibn Mo'een and Ibn Taymiyyah did not accept it because of the doubt in the narrators beside contradicting Quranic verses. Even those Sunnis who accept this narration say that it does not mean at all that it is Makrouh to wear new clothes on Tuesday.
We need to warn people from baseless claims in the name of religion.
Yes, you can wear new clothes on any day.
And Allah knows best.
Yes, it is allowed to cut nails on a Tuesday.
For further information about cutting of nails, please refer to this Q&A:
And Allah knows best
No, nor any other day for that matter