All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
First of all, may Allaah reward you for your good intention and for being keen on making Da’wah. There is no doubt that the Internet is one of the important means of Da’wah and education. Indeed, Allaah has guided those who call to Him by facilitating for them the Internet in order to use it in a better way so that the voice of Islam and the truth would reach all corners of the world. There is no doubt that a person who calls to Allaah should do so with knowledge and insight; Allaah Says (what means): {Say, "This is my way; I invite to Allaah with insight, I and those who follow me. And exalted is Allaah; and I am not of those who associate others with Him."}[Quran 12:108]
However, this does not mean that a person does not call to Allaah until he becomes a scholar; rather, he is only required to know the issue that he calls to and the matters that are related to it. ‘Abdullaah Ibn ‘Umar narrated that the Prophet said: “Convey on my behalf even if it is (only) one verse (from the Quran)." [Al-Bukhari] Besides, if there is no benefit in revealing your name, then it is better to conceal it.
As regards your second question, what is required is that a correct Ghusl is performed in any manner; so it is permissible to have a shower for this purpose and it is not necessary to pour water with a bucket. For more benefit, please refer to Fataawa 85754 and 91182.
On the other hand, a Muslim should avoid being extravagant in using water; Allaah Says (what means): {…and eat and drink, but be not excessive. Indeed, He likes not those who commit excess.}[Quran 7:31] Moreover, Anas said: “The Prophet used to make Ghusl with a Saa’ to five Muds and he used to make ablution with one Mud.” [Al-Bukhari] [A Saa’ equals 4 Muds and a mud equals 750 grams approximately]
As regards your third question, then our answer is that you should try to combine between Islamic studies and academic studies, and this matter has become easy, either through Islamic satellite TV channels that transmit lectures and courses of knowledge or through the Internet. For more benefit, please refer to Fataawa 89887 and 84726.
Allaah Knows best.