This is a word transliterated and adapted from Greek παρεκβολή (parekbolḗ), from πᾰρά (para-, "near", but here meaning "placed together") and ἐκβολή (ekbolḗ, "throwing out" but here meaning "something tossed off"), which together can be a "compilation of a set of critical remarks":
I. digression, lamb.Bab.8.
II. compilation of a set of ...
Filius, i means "son"
Liberi (masc. plur.) means "children" and more precisely children of free people, i.e. not slaves.
This family has 2 sons but 3 children. There probably is a daughter around somewhere.
From an entry (which includes references here omitted) in Döderlein's Hand-book of Latin Synonymes:
Citus; Celer; Velox; Pernix; Properus; Festinus. 1. Citus and celer
denote swiftness, merely as quick motion, in opp. to tardus, ... velox
and pernix, nimbleness, as bodily strength and activity, in opp. to
lentus; properus and festinus, haste, as the ...
Dictionaries are notoriously bad at describing sex acts. Thankfully, J. N. Adams rectified that with his The Latin Sexual Vocabulary (Baltimore, 1982). I can add little to what he says of the two words (p. 136–137):
(vii) Criso and ceueo
Latin possessed two technical terms for types of sexual motion (in both cases that of the passive partner), criso and ...
I would say, in a sense, tandem is little different from the rest, as tandem tends to imply pressure that was accumulating and being released, or something that was expected and finally happens (i.e. Not necessarily after sequence of events). Thus, you can see tandem used to intensify a question to indicate asker's stress. Practically speaking, in the title ...
pŏpīna is the one, borrowed from Oscan or Umbrian, and cognate with (native Latin) coquina. Indeed, a Packhum search gives no results for thermopolium and 54 results (59 matches) for popina - note that, still, thermopolium can be found e.g. in Plautus and Petronius.
Note that caupona and taberna were also common, but while L&S lists them as synonyms, ...
I think there is a clue in the sive which separates the word from excerpta.
Sive was once customarily used to mean 'or' when giving an explanatory sub-title to a more obscure name. For example, the well-known Gradus, popular in various editions and more or less contemporary with your Oxford University example, had the full title Gradus ad Parnassum, sive ...
Incidentally, starting with Augustus, having three children was honorable and gave men "certain political advantages", whereas having less than three children "restricted a man's ability to accept inheritances and legacies" (Edmondson 2015: 576).
See more on ius trium liberorum in Wikipedia or in Edmondson 2015.