Purity (Arabic: طهارة, Tahara(h) ) is an essential aspect of Islam. It is the opposite of najis, things which are considered ritually impure are in the state of najāsa.
If the down side of the shoes becomes Najis, then walk ten steps after removal of the Najis item, lower part of the shoes becomes Tahir.
'If the upper part of the shoes becomes Najis, you must wash it with water after removing the Najis item if any.
As Muslims, we do istinja`, or wash ourselves after using the toilet, not only because it is more hygienic and cleaner, but also to stay in the state of taharah, especially for salat.
This is necessary, wherever you may be, even in public office, if you are there regularly. You can use a water bottle, and it does not need to be excessive amount of water as well.
If you do not wash yourself, then no, you cannot pray in such a state, especially if it is after urinating. Your option is to either wait until you go back home, wash yourself, and then pray, or do as recommended above, and pray on time.
And Allah knows best.
Simply, everything is Taahir for you unless and until you know for sure that it is Najis. This is a rule in jurisprudence based on a narration of Ammar from Imam Jafar Al-Sadiq (AS) stating : Everything is ritually clean till you know that it is ritually unclean. (Wasaa'il al-Shia, V.2, Section 37 on Nijasah).
Your doubt in this matter does not make any difference. You are ritually clean because you are just doubting and not sure that your body became Najis.
We have covered the topic of waswasah and doubts in tahara a few times, and you are able to search in the Q&A on the topic of waswasah and taharah.
The simple rule of thumb is because you are doubting, you consider it all to be tahir. Nothing more.
Please watch this clip, which is a part of a lesson I gave on taharah and najasah. Hope it will be of benefit.
She must perform Ghusl and Wudhu and pray and fast. Ghusl is obligatory before Fajr for medium Istihadha.bin excessive istihadha Ghusl is obligatory three times; before Fajr prayer and before Dhuhr prayer and before Maghrib prayer.
She is not allowed to leave fasting or leave praying just because of Istihadha.
The question of : where is Quran is not proper if Muslims understand the Quranic order ( Obey Allah, obey the Messenger and your divine leaders)(4:59).
You can ask this person: Where it says in Quran to pray morning prayers in two Rak'ats, Dhuhr in four, Assr in four, Maghrib in three and Isha is four? The answer is: The Prophet Muhammad (SAWA) said that and Quran ordered us to obey him.
The Prophet (SAWA) said in Hadeeth al-Kisaa' which is narrated by many authentic narrators in Sunni and Shia books that Allah has created the universe for love of Ahlul Bayt (AS).
Allah (SWT) Has kept every Infallible totally pure, and kept any type of impurity far away from them, not that Allah has removed impurity from them, but kept them far away from any impurity i.e. Allah did not allow any impurity whatsoever to come near any Infallible. Quranic verse 33:33 stated: In fact, Allah wants to keep impurity away from you O, Ahlul Bayt إنما يريد الله ليذهب عنكم الرجس أهل البيت
There is a big difference between ليذهب عنكم to drive away any impurity from coming near you, and ليذهب منكم which means to drive away impurity from you which can mean driving away any existing impurity. Allah (SWT) never said that, but He said ليذهب عنكم which means that Ahlul Bayt never had any impurity, and Allah kept impurity far away from coming near them.
All the existence of the Infallible is absolute pure in the highest level which can never be compared with ordinary pious people.
These facts are very clear in Quran and the authentic Hadeeths. After believing in these facts, we do not need to go into details of the personal life of the Infallible, which are not necessary for us as it has nothing to do with our faith and practice and our responsibility to be sincere and humble servants of Allah and obedient followers of the Prophet (SWT) and Ahlul Bayt(AS).
After removing the blood, one time washing with tap or Kurr water is enough and two times with Qaleel water.
Dog is Najis whether it is used in hunting or guarding or otherwise.
Islam does not say that it is not allowed to have a dog as a pet, but it clearly says that dog is Najis and you must avoid any Najis item, otherwise your Prayers might be invalid if your cloth or body is Najis.
Hunting and guarding dogs are out of home usually, so there is no risk of Najasah on you from such dogs, but when the dog is at home as a pet , the risk is there.