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.
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 mentionsdoes 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 sacrific eofferedsacrifice offered to) the Fathers, and marriage.
However, the same Grihya Sutrastext 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).