It is not mentioned anywhere that kunkumum is to be offered. So, it is not a must. Only the offering of sandalwood paste is mentioned. We have addressed a related detail before – kumkumum is not an original substance. Hence it is enough if sandal wood paste alone is offered. Not sure when you say kumkumum, whether you are referring to saffron (Kunkuma poo). If so, it can be included while griding the sandal wood paste. Or if you are referring to kumkumum purchased from shops, no need to offer that.
Recitation of Azhvar pasuram-s during Tiruvaradhana sevakalam is part of Vadakalai tradition and is followed everywhere. In all houses, there is no Tiruvaradhanam without Tiruppavai recitation.
Not sure why you have this doubt as all traditions follow the same practice during Tiruvaradhanam. At all houses, there is not Tiruvaradhanam without Tiruppallandu, Tiruppavai (cittrancirukaalE, etc.) during satrumurai.
The term ‘Simha’ connotes superiority/eminence – Simhasanam, Purushasimham, etc. Among the animals, the lion (Simha) is the supreme, king of animals. Perumal is superior and supreme. Raghavasimham is a divine name of Perumal. All His entourage are superior.
We are aware of Garudman. Among his vahana-s, simha vahana is superior. This is the perspective from which this should be viewed and from a demi-gid perspective. Even when demi-gods have Simha vahana, it does not mean that Garuda should not have one. At that same time, Garudman must not be installed in the temples of demi-gods as he is the eternal resident (Nityasuri) and is mentioned as such in the Vedas. As per the purana-s he is the vahana of Perumal. Mahabharata mentions his divine history and that he sought a boon that must be a servitor only to the Bhagavan and be His vahana. Hence he must not be consecrated in the temples of demi-gods.