Is septum piercing allowed in Islam?

There is no problem as per Ayatullah Sistani

Can you please suggest me any sight or any book in which purification bath for periods is listed. Because there are different ways and I’m so confused.

Please check the following website of Sayed Sistani:

https://www.sistani.org/english/qa/01198/

Question: How is a Tartibi (sequential) Ghusl done?
Answer: In this method of Ghusl, a person should first make a Niyyat (intention) for Ghusl. Thereafter one should first wash one's head and neck, and thereafter the remaining parts of one's body. It is better that one washes the right part of the body first and then the left part. Furthermore, based on obligatory precaution, it is not sufficient to make the intention of Ghusl when moving the head, neck or body while they are already under the flow of water, rather, the part that one wants to perform Ghusl on - in the event that it is already under the flow of water - must be taken out from under the flow of water and then washed with the intention of Ghusl.

Is it allowed for women to remove body hair with gents razor for safety?

No problem

I have a question regarding Istihadha(due to taking the pill).
How can I exactly know if i have major or medium Istihadha? Can I use a tampon and check before the prayers? If its completely soaked is it medium or major Istihadha? And whats the law if I'm not able to do ghusl before prayer? Does wudhu suffice or do I have to make up the prayers?
And also i will be going to Ziyarah in a week InshaAllah. What are the things that i can't do or the places I cant go? Also if you're on istihaza can you go inside the haram of the masoomeen and touch the zarihs?

The timing to check whether istihadha is little, medium or excessive, one must check at namaz time. Take a ball of cotton and place it on the surface of the vagina. If the blood is only on the surface of the cotton then it is little istihadha. If it penetrates the cotton then it's medium. If the cotton gets completely soaked with blood and flows out from it within a few seconds then it's excessive istihadha. With a tampon, it can stay for 1-2 hours hence one is unable to check with it while it's inserted. The above steps must be carried out to determine type of istihadha unless you know which type of istihadha it is in which case the above steps are not necessary.

Entering the zarih room and masjid is no problem for a person in istihadha however it is haram for a person in haydh.

I'm taking a contraceptive pill and wanted to know if the bleeding in the break when you take a week off after taking the pill for 21 days is considered hayz or istihaza?
And if I have major istihaza can i use a tampon after taking a ghusl before praying or entering the shrines so the blood doesn't flow out(and later taking it out when im done) or is it okay with just a pad?
If I dont have the opportunity to do ghusl while traveling what can i do for the prayers?
I'm just a bit concerned, i dont want to do it wrong on ziyarah

After 21 days of no bleeding, if the bleeding which starts meets the criteria of haydh, then it should be taken as haydh. Criteria of haydh is bleeding should be for a minimum of three days and for the three days, bleeding should have continuity. If the bleeding goes over 10 days or there is a gap of less than 10 days between two separate bleedings , then it will be istihadha

In regards to going to the zarih, it makes no difference whether you use a tampon or pad. It is allowed. If your bleeding is haydh, then it is a problem going to the zarih whether you use a tampon or not.

During travel, usually water is available unless you feel that the water would be detrimental to your health for example if it's winter and is cold or similar problems. In this case you can do tayammum instead of ghusl.

I was doing zohr prayer, and I was in my second rakat and when I was doing the second sajda, I doubted that in the first Sajda I said "azim" instead of "aala".
So can I correct it with Sajda Saw or Namaz Ehtiyat ? Or should I perform my prayer again ?

In the dhikrs of namaz, if you make a mistake while you are reciting it and if you realise it, just repeat the dhikr. If you have finished and gone onto the next action as is in your case, then there is no problem and you don't have to repeat the namaz nor do you have to do sajda e sahw.

I also wanted to ask you how must the ruku and sajda be performed? For example in Rukku to what extent one should be bended
Or in Sajda is it okay if my elbow touches my knees ?

For rukuu, one must bow to the extent that the fingers reach the knees.
For sujood, there are 7 parts of the body which is wajib for them to touch the ground that is the forehead, two palms, two knees and the two big toes. As for the elbows touching the knees in sajda, there is no problem

Fajr qaza time is when it is sunrise time right ? Or it’s before that ?

At sunrise

Jab Ham zyarate Ashoora padte h unme kahi jagha kuch ayat sajde me padni h or kahi jgha likha h kadam age rakh kr pade or piche rakh kr. Ye amal ashure ke din ka h. Mera masla ye tha agr ham aam Dino me Zyarate Ashoora padte he to sajda Jha ata he zyarate ashoora ke ander Am dino me bhi krna padega or back an forwrd bhi jana zarury he?
Ya bus ye Ashoore k Amaal jab ham log padhte he fakat usi din h?

If you look at Mafatih you Jinan, Allama Majlisi only narrates the sajda as part of Ziyarat e Ashura

Can a girl/woman pluck her eyebrows without wearing any makeup?

Yes she can