If the virginity was lost by adultery or any reason other than religious marriage, then the woman is still considered as virgin and it is not permissible to marry her permanently without the permission of her father or paternal grandfather. Also it is not permissible to marry her temporarily and consummate the marriage without the permission of the father or the grandfather. Yes, it is permissible to marry her temporarily without the need to seek the consent if the marriage is not consummated.
A Kaffara is not obligatory in the said case.
The organ of urination can only be purified with water. Toilet papers can be used to make it anus tahir by wiping it with three papers. Based on an obligatory precaution one must use paper thrice even if the najasah is removed before that. If the excrement has spread around the anus more than what is usual, water must be used to make the area tahir.
Islam is a divine religion that Almighty Allah revealed to guard the welfare of people. Almighty Allah knows the reality of things and what benefits His slaves, so He set laws accordingly for them to observe. Since Islam is the seal of religions, these laws are for until the end of this world. Because of corruption, badness and evilness in certain things or acts, He commanded us to refrain from them and made them prohibited. Similarly, because of benefits and goodness in certain other things, He ordered us to perform them and made them obligatory on us. Some of these laws are general and apply to all people, all the time, and anywhere.The ability of the human being is limited, so is unable to find out and understand the reasons behind the Sharia of Almighty Allah. Sometimes Allah Almighty has taught us through the Holy Prophet and the Imams (peace be upon them), the wisdom behind certain few rulings. We must obey His laws by refraining from the prohibited acts and undertaking the obligatory acts, even if we do not know the reason behind each and every one of them.The najasah of the dog is one of the rulings about which we do not know the wisdom behind.