Du'a (Supplication)

Yes, it is authentic and narrated in many authentic books. Allama Majlisi narrated it in Biharul Anwaar, volume 99, page 247. Dua Tawassul was narrated by Mohammad Bin Babawayh from Infallible Imams.

There are always persons who create doubts because of their own misunderstandings or way of thinking, but their doubts are for them only, because our leading scholars who have much more knowledge like Allama Majlisi and leading Maraaji' are the scholars to be followed.

Wassalam.

It is recommended to praise and glorify Allah and recite Salawaat before Du'a, then recite Du'a or supplicate to Allah (SWT) seeking your need, then recite Salawaat after Du'a.

It is highly recommended to pray for your parents , relatives and Mo'mineen before or with praying for yourself.

Wassalam.

It is permissible to recite Du'a Tawassul during Sajdah because the Sajdah is only for Allah (SWT) and never for any one else but Allah. During Sajda Sahw, we recite (Bismillah a Billah, Assalamu Alayka Ayyuha Annabiyyu Wa Rahmatullah Wa Barakatuh). It does not mean that we doing Sajda for the Prophet (SAWA) but for Allah (SWT) only. Addressing the Prophet or any Ma'soom during Sajdah does not make the Sajdah for him at all but it remains always for Allah (SWT). It menas hat you are talking to them while prostrating to Allah (SWT).

Wassalam.

Repeating Estighfaar is very helpful as well as repeating LA HAWLA WALA QOWWATA ELLA BILLAH.

When the believer remembers the fact of the grave which is our place for long period, and remembers the Paradise for the pious and Hellfire for wrongdoers, it should make him away from sinful acts.

It is good to recite these Quranic supplications (RABBI A'OOTHO BIKA MIN HAMAZAAT ESH SHAYATEEN WA A'OOTHO BIKA RABBI AN YAHDHOROON). 

Also this supplication (ALLAHUMMA AKHRIJ HUBBAD DUNYA MIN QALBI)

It is also useful to remember the end of those who committed sexual sins and got nothing but disaster in this life and hereafter. That should be enough lesson for every sensible person.

Wassalam.

Du'a Mujeer is one of the authentic supplications narrated from the Prophet Muhammad (SAWA) from Jabraeel (AS) when the Prophet was praying in Maqam Ebrahim which is in front of the Ka'bah.

Du'a al-Mujeer is narrated by our prominent scholars like al-Kaf'ami inAl-Balad Al-Ameen  and Al-Misbah.

Wassalam.

Yes it is valid. Reciting Du'a of fasting is not obligatory but just recommended.

Wassalam.

There are many supplications to avoid harm and get protection from harms like: 

1. Repeating Estighfaar ( ASTAGHFIRULLAH RABBI WANATOOBU ELAYH).

2. Repeating Salawaat ( ALLAHUMMA SALLI AL MOHAMMAD WA AALI MOHAMMAD).

3. Repeating ( LA HAWLA WALA QOWWATA ILL BILLAH ).

4. Ziyarat Ashura every day.

5. Night Prayer every night.

and many other recitations.

Wassalam.

Our leading Ulama who have vast knowledge and long experience in Hadeeth believe that Du'a al-Faraj and Du'a al-Nudba are authentic, that is why they read and advise the believers to read these Du'as.

Du'a e Faraj (ALLAHUMMA KUN LIWALIYYAK AL HUJJAT IBN AL HASAN .....) is narrated by the prominent scholar Al-Kulaini. From Mohammad Ibn Easa ibn Obaid through Ali Ibn Ebraheem and all of them are authentic narrators. Mohammad Ibn Easa ibn Obaid is well known narrator from Imam Mohammad al-Jawad (AS).

Du'a e Nudba was narrated by Mohammad ibn al-Mashhadi is his very well known book Al-Mazaar al-Kabeer. He narrated it from Mohammad ibn Abi Qurrah who narrated it from Mohammad Ibn al-Husain al-Bazoofari who is from the teachers of al-Shaikh al-Mofeed, and from the teachers of Ibn al-Ghatha'eri as Ayatullah Khoo'ee mentioned in Mu'jam Rijaal al-Hadeeth. 
Wassalam.

It is Makrouh (disliked) to look at the sky whilst praying Salaah. We have clear evidence in Hadeeth stating not to do it, Obviously, every Makrouh (disliked) is permissible but it decreases the reward. It is recommended whilst praying Salaah to look at the place of Sojood when you are standing Qiyaam.

Wassalam.