The Grihya Sutras are scriptures that detail the rules and regulations regarding Vedic domestic rituals for householders (Griha - House in Sanskrit). There are various such Sutras written by different people e.g. Ashwalayana, Drahyayayana, Gobhila, Hiranyakesin, Katyayana, Khadira, Latyayana, Paraskara, Sankhyayana and Apastambha is one of them.
Parts of the Apastambha Sutra:
The entire text is divided into 30 sections, called Praśnas or questions - The first 24 talk about the Srauta or Vaitanika sacrifices, beginning with the simplest rites, the new and full
moon offerings, and ending with the complicated Sattras or sacrificial sessions, which last a
whole year or even longer.
The 25th Praśna contains the Paribhāshās or general rules of interpretation which are valid for
the whole Kalpa-sūtra, the Pravara-khāṇḍa, the chapter enumerating the patriarchs of the
various Brahmanical clans, and finally the prayers to be recited by the Hotraka priests.
The 26th section gives the Mantras for the ceremonies for which the sacred domestic or Grihya fire is required, the 27th the rules for the performance of the latter and the next two the aphorisms on the sacred law.
The last and 30th Prashna is formed by the Sulabha-sutra, teaching the geometrical principles, according to which the altars necessary for the Srauta sacrifices must be constructed.
Coming to the second question, yes the Apastambh Grihya Sutra does mention that cattle may be slaughtered when a guest arrives, or at the occasion of marriage or as an offering to the ancestors in the Shraadh ceremony and I am sharing the relevant verse here:
9 These are the occasions for killing a cow: (the arrival of) a guest, (the Ashtaka sacrifice offered to) the Fathers, and marriage.
However, the same text ALSO give the option of letting the cow loose when a guest arrives so that the host does NOT have to sacrifice it to entertain the guest. At multiple places they suggest that cow's flesh should be substituted with that of a goat or a ram or even better, cooked grain or payasam (kheer in Hindi).
17 If the guest chooses to let (the cow) loose, he murmurs the next (formulas, II, 10, 8-11) in a low voice (and says) loudly, 'Om! Let it loose!' (II, 10, 12).
18 (In this case) he recites the next (formulas, M. II, 10, 13-17) in a low voice over the food which is announced to him (instead of the cow), (and says) loudly, 'Om! Make it ready!' (II, 10,18)
There are other verses too that mention the sacrifice of bovines but not really cows. For example Rig Veda verse 10.85 does mention ritual sacrifice of oxen but no cows. I could find only one verse where cow, that too a barren one is supposed to be offered to Agni along with Ram or Oxen Rig Veda verse 10.91.14. And again the verse talks about a sacrifice being offered to a god NOT for the consumption of humans.
14 He in whom horses, bulls, oxen, and barren cows, and rams, when duly set apart, are offered up,—
To Agni, Soma-sprinkled, drinker of sweet juice, Disposer, with my heart I bring a fair hymn forth.
15 Into thy mouth is poured the offering, Agni, as Soma into cup, oil into ladle.
Vouchsafe us wealth. strength-winning, blest with heroes, wealth lofty, praised by men, and full of splendour.
You should also know that there is a tradition in India of considering guest as gods - Atithi Devo Bhava implies guest is equivalent to god. Hence these verses have to be understood in that context.
The purpose of these verses is to make people understand that a person should not hesitate to sacrifice even his most precious possession for the sake of a guest. However there is a loophole in the next verses where alternatives are clearly mentioned if the guest so desired.