First of all What is Ratha Saptami?
The Sukla Paksha Sapatami Tithi day in the Magha month is known as the Ratha Saptami.It is dedicated to the worship of Surya Deva.As per Puranas Surya started illuminating the whole world on this day and hence the day is also called "Surya Jayanti".
In general taking bath during Arunodaya muhurtha(sunrise time) is
highly auspicious in the entire Magha month.
The Snaana Kaala should be at Arunodaya to Praatah kaala; it is
emphasised that bathing in the waters at the time of Suryodaya would
purify even those who are the sinners of Brahma hatya or Suraa paana;
any human being irrespective of caste, age or sex could take Maagha
What rituals has to do and what activities/ celebrations/ rituals?
As said before the day is dedicated to Surya Deva.So the activities are related to him only.Following are the 2 highly rewarding & recommended activities for that day:
1)Arunodaya Snaana(Bathing during sunrise)
The Snaana Mantra-ada Janma krutam paapam mayaa janmasu Janmasu, Tanmey Rogam cha shokam cha Maakarihantu Saptami/ Yetatjjanmakrutam
paapam yaccha janmaantaraarjitam, Manovaakkaayajam yaccha
jnaataajnaatey cha ye punah/Iti Sapta vidham paapam Snaanmey Sapta
Saptikey, Sapta Vyaadhi samaayuktam hara Maakari Saptami / (May the
entirety of my sins accumulated in my present and previous births on
account of conscious and unconscious acts or those perpetrated by my
vocal or mental roots be dissolved on this Makara Saptami and may this
Sacred Snaana with my earnest and heartfelt supplications and
obeisances to you Surya Deva, in the form of Seven kinds of Sins and
Seven types of Diseases be destroyed for ever!)
2)Argya Pradana(water offerings to Sun god accompanied by Mantras):
Arghya Pradana Mantra:
Sapta Saptivaha preeta Saptaloka pradeepana, Saptami sahito Deva
gruhanaarghya Divaakara/ (Divaakara! You are affectionate of riding
on the chariot drwan by Seven Horses with Seven Names and bestow
splendour to Seven Lokaas obviously fond of the numeral of Seven;
Bhagavan! may I have the privilege of offering ‘Arghya’ on this
Saptami Tithi to mark my reverence
Is Tila Tarpana(Pitru Tarpana) a recommended act on Ratha Sapatmai?
From the second link:
Maagha Shukla Bhishmaashtami is obeserved with Bhimoddishya Shraaddha
Tarpanaas only by those Grhastis who have children alive; but
otherwise considered as compulsory. But Maagha Shukla Dwadashi is to
be noted as significant for Tila Snaana, Tila Puja to Vishnu, Tila
Naivedya, Tila Taila Deepa Daana, Tila Homa, Tila Daana, and Tila
So ,as you can see the Magha Sukla Bhishma Ashtami is recommended for Pitru Tarpanams.And of course the Magha Amavasya Tarapanams are also considered highly auspicious.But, since nothing is mentioned specifically about doing Tarpanams on Ratha Saptami it can be assumed that it is not recommended.
And, about the house warming thing,i can't answer.I can't answer regarding things that are not be done on this day either.So consider this as a partial answer.