I live in a very hot and humid region. Is it permissible for me to wear minimal clothes while alone and inside? Also what is the ruling on sleeping naked alone and with a partner (spouse)? Also is it necessary for women to cover their awrah while performing wudhu? I mean it would prevent her from properly washing her forearms and head.
All Praise to Allah Subhanahu wa Taala and blessings of Him be on Prophet Muhammad peace be upon him His family and companions,
Narrated Bahz bin Hakim: "My father narrated to me from my grandfather, who said: 'I said: "O Messenger of Allah! Regarding our 'Awrah, what of it must we cover and what of it may we leave?" He said: "Protect your 'Awrah except from your wife or what your right hand possesses."' He said: "What about a man with another man?" He said: "If you are able to not let anyone see it, then do so." I said: "What about a man when he is alone?" He said: "Allah is most deserving of being shy from Him."(Tirmidhi)
Our scholars have mentioned it clearly that awrah should be covered if there is not any necessary conditions to avoid even when person is alone it is preferred to do it and while sleeping it is preferred to cover oneself with a sheet if naked,Regarding your query about covering awrah while performing wudhu so it is important to know that The fard of wudhu includes masah of head and washing of arms and awrah would be exposed during this masah and washing so women should not perform wudu in the presence of non-mahram due to the exposure of her awrah.
Also see this answer:
Imam Zayn Ibn al-Nujaym said in his al-Bahr al-Ra’iq:
“Know that there is scholarly consensus (ijma`) that it is obligatory to cover one’s nakedness (awra) in front of others… And when alone, there is difference of opinion [as to whether it is obligatory], but the correct opinion is that it is necessary (wajib), unless the uncovering was for a valid reason, as mentioned in Sharh al-Munya.” [al-Bahr al-Ra’iq, 1: 283]
Imam al-Haskafi said in “Durr al-Mukhtar,” “[To cover one’s nakedness] is a general obligation, even when alone, according to the correct opinion, unless it is for a valid reason.”
Ibn Abidin explained in his Radd al-Muhtar:
“‘Even when alone,’ that is: outside of prayer it is obligatory to cover one’s nakedness in front of others by scholarly consensus, and even when alone according to the correct opinion…
“Now, the apparent meaning of covering one’s nakedness when alone outside of prayer [in this context] is that which is between the navel and knee, such that even women do not have to cover other than that [when alone] even if it is of their nakedness (awrah) [in front of others]…
“‘According to the correct opinion,’ for Allah Most High, even though He sees the covered just as He sees the naked, sees the one whose nakedness is uncovered as leaving proper manners, and sees the one covered as exhibiting proper manners. These proper manners [here] are obligatory [f: because of the primary texts about them] whenever there is ability to exercise them.
Allah Swt and His Messenger knows best.