Is there any specific reasons for Tarpanam (rituals for the Pitrus) being performed during Amavasya /Poornima days?

The gravitational force that the earth exerts is high on these days and hence it is believed that the Pitru Loka is closer on these days. That is why special rites for the Pitrus are performed on these days.

It is said that we do not have any choice of choosing our family/parents and it is all determined by our previous vasanas. If this is the case then why do our elders say that if parents do not do their nithya karma, it will affect their children? It is not the children’s fault that their parents are not doing their karma. Please advise.

Every jiva is born into a particular family/situation only on the basis of their karma. If a jiva is very sattvic, he is born to parents who are sattvic. if a jiva is carrying a lot of sins and has to experience them, then his birth occurs in a situation where he has to suffer. The former is born to the latter as a child and they both experience their karma. If a jiva has acquired to sins in this life, that has to result in a birth with some disease. There is this other jiva who has to experience his karma load by taking care of such a person with such a disease, then their vasanas/karma bring these two together.
A son would naturally inherit his father’s wealth and property, he would like to have everything that is good from his parents. wouldn’t he? when that is the case, logically, the sins are also passed down generations.

My father passed away a few years ago; since then every year I have been doing shradh; How long this should be continued? How far do my offerings benefit my father? I understand he will take rebirth. Will my offerings go waste once he takes birth?

You are supposed to perform Srardha for your deceased father throughout your lifetime. There are perfect arrangements in the nature for your offerings to reach the ancestors.
If you do the rites and rituals properly, it will help him to a certain extent. A mantra in the Srardha itself says, ‘if the dead soul has taken another form, let my offerings be transformed and reach the soul in a form that can be consumed by the form (like grass for the cow or horse-gram for the horse etc.)’

Sri Swamiji has, in his works, mentioned that the articles for performing rites and rituals are no more pure. I am living in a foreign country for the past 25 years. Do the rituals performed in a foreign country have any benefit?

Even in India, the rites and rituals are losing its significance as it is next to impossible to strictly adhere to the rules as prescribed by our scriptures in performing them. The requisite materials are no more available nor the householder who performs these rites has any caliber to do them. No one can be blamed for this, as it is the situation that warrants so many compromises to be made.

Gayatri Mantra is also recited when offering Nyvedyam to God. Is it contain the same meaning? Is not Gayatri supposed to be chanted by men after Upanayanam alone? What is meant by ‘Pranaya Swaha, Apanaya Swaha ..’ etc.?

In earlier days, it was a belief that Vaideeka Pooja (Pooja according to the prescribed Holy Texts) should be performed only after Upanayanam. Hence, Gayatri Mantra is used in this.
The five aspects are the Pancha Praanas – Praana, Apaana, Vyaana, Udhaana and Samaana, and the last offering is to the infinite Brahman.

While performing rituals, pujas etc. we are unable to repeat the Mantras which the pundits say. We are aware that we are making lot of mistakes. When we are unable to repeat it correctly, can we simply we say “Krishna”, “Krishna”, instead of saying the mantras wrongly? How to get over this genuine difficulty?

You are right. That is the very reason why we are advocating that the Mahamantra is alone enough in the place of all pujas and rituals.

We perform Shrardhas and Tarpanam for the deceased. How do we know that they are not suffering? How do we know how they are reborn?

If at all the soul of the deceased undergoes sufferings, it is indicated in the dreams of their relatives.
In general, one who has performed advanced spiritual Sadhana discerns what was the earlier ‘janma’ of a soul, what form the soul takes and so on. It is not discernable to the common man.
Once when Swami Vivekananda visited Chennai, he was haunted by a host of spirits (astral bodies of the dead). They came to him and cried, requesting him to deliver them from their sufferings. Swamiji went to Marina beach and took some sand in his hand and offered it into the ocean praying for liberation of these spirits, by virtue of his meditative powers.
It is said in the Shastras that the offerings that one gives during Tarpanam (like water and sesame) reach our ancestors in the form that they can consume – for eg., grass, if they were born as a cow, blood if they were born as demons and so on.

In the event of a death in the family, going to the temple is prohibited. Why?

Generally, temples are prohibited for only 13 days, after which you can visit other temples, except for Maha Kshetras.
Generally we offer cooked food for the Lord, while ‘Pitrus’ (manes) prefer only half-boiled food. Melodious music pleases the Lord while the dead are happy with the sound of wailing. We do not wear wet clothes while we pray to the Lord while the Pitrus should be propitiated wearing wet clothes. God takes only little of what is offered to Him while the Pitrus consume a lot. God likes flowers and ‘kolam’ (Rangoli) and the dead hate these. God likes celebrations while the Pitrus don’t.
Generally after a death in the family we don’t do that which is not liked by the dead. Hence we avoid going to temples.

My current work needs me to leave for the work before sunrise. Can Amavasya Tarpan be performed before sunrise?

No Amavasya Tarpanam cannot be performed before sunrise. So the only alternative is to chant the Mahamantra and pray for your parents. That is enough.

If a person does not have any children, who will perform his last rites? If someone related to him does the last rites, will his soul get liberated? Who will, for him, do the monthly and yearly rituals?

If one does not have a male child but has a female child, then getting the holy grass (‘dharbai’) from the daughter, some one else can do his last rites. His son-in-law or his brother’s son can do the last rites, as also someone whom the person might have adopted during his lifetime, or someone that the deceased considered ‘abhimana putra’.
The person who does the last rites also should perform all the subsequent rituals.
However, anyone can perform his last rites by chanting the name of Govinda thrice (this is called ‘Govinda Kolli’). If this is done, there is no necessity to perform any subsequent rites or rituals.