Water is a transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's streams, lakes, and oceans, and the fluids of most living organisms. It is vital for all known forms of life, even though it provides no calories or organic nutrients.
Not in most cases. Wiping would not suffice when purifying, and "washing" must be done, even if it is a very small amount of water, as long as it is "washed".
There are certain laws related to using something other than water when doing istinja` from extretement of faeces. The details of this you must read in the book of laws of your Marja' taqleed.
However, in general washing must be done.
And Allah knows best.
Being under the water for 5 minutes would, in most, if not all cases make water reach all parts of your head, and that would be enough for your ghusl. The important thing is you follow the correct procedure of ghusl, which is head/neck, then right side of body, then left side of body.
Avoiding excessive doubt is also very important.
And Allah knows best
Quranic verses in Sura Yousuf are the strongest evidence in this matter.
Prophet Yousuf told his brothers: Take this shirt of mine and cast it on the face of my father, he will turn clear-sighted. (12:93).
'We have many authentic narrations on the blessings which can be obtained by touching (Masah) of blessed items like Black stone, Zareeh of most humble servants of Allah, Quranic text, etc.
Hair does not to be completely dry for Mas-h in Wudu. Water remains on the hands should overcome the moisture or wetness on the hair.
When the shower water is continuous then it is connected with the Kurr and has the rule of Kurr water.
Drinking in copper vessels is allowed as far as the vessel does not have any rust on it and is not gold plated or silver plated.
It seems from some references that it is like a medication, so it should not be repeated more than what is required. There is a narration in Mawsoo'at Al-Hadeeth Al-Tibbiyyah موسوعة الأحاديث الطبية ( Ecylooedia if medical narrations) discouraging drinking water in copper vessels as a habit because it can cause some harm.
You can put it is any will or water near your area. If there is no water at all, then you can burry it.
Ghusl does not need water flowing on the body, but needs just making any amount of water reach to every part of the body even by wiping water on all parts of the body. A big scholar in Najaf Ashraf who is Ayatullah Sayyed Muhammad Husain Al-Hakeem said: Ghusl can be performed with one cup of water by putting my hand in the cup of water then wiping over my head, face, neck, right side of body then left side of the body. Making the water touch by wiping to the whole body won't take more than one cup of water.
You can refer to Islamic rules of your Marja' of Taqleed for more details.
Ghusl does not need to be done in the shower, but it must be "washing", and water flowing, or to submerge yourself completely under water "ghusl irtimasi". Wiping in front of a sink would not be considered as ghusl, and therefore invalid.
And Allah knows best
Just touching any impure part of the body during performing a Ghusl does not invalidate the Ghusl.
It is permissible to wipe off the water of Wudhu, but it is recommended to leave it to dry by itself. The Hadeeth narrated from the Prophet (SAWA) states: Who performs Wudhu and wipes its water will get one reward, and who performs Wudhu and does not wipe it will get thirty rewards. (Thawab Al-A'maal by al-Sadouq, page 32.)
Sorry to hear about your situation. Inshallah it improves soon, by the grace of Allah.
As Shaykh Zoheir said, you can do wudu from a bottle of water. Perhaps you can step out of the car for prayer if it is safe.
If you have a concern about being seen without hijab, just do your best to preserve your modesty as wudhu can essentially be done from under a cloth.
The larger tahara can also be done with a reasonably small amount of water (rather than requiring an actual shower), but for this, modesty is more important of course. I guess you and your husband will have arranged somewhere or some way to wash up.
If you absolutely cannot perform wudhu or ghusl due to modesty reasons, you ca do tayammum.