Pausanias Analysis

πλησίον δὲ ἅρμα τέ ἐστι χαλκοῦν καὶ ἀνὴρ ἀναβεβηκὼς ἐπʼ αὐτό, κέλητες δὲ ἵπποι παρὰ τὸ ἅρμα εἷς ἑκατέρωθεν ἕστηκε καὶ ἐπὶ τῶν ἵππων καθέζονται παῖδες·

The first clause has ἅρμα as subject of ἐστι, with χαλκοῦν predicative; ἀνήρ is coordinated as a second subject-like nominative with participial modifier ἀναβεβηκώς. In the second clause, κέλητες ἵπποι is an appositional/predicative description, with εἷς ἑκατέρωθεν modifying the horses; ἕστηκε is singular despite the apparent plural phrase, so the attachment is somewhat uncertain. παῖδες is the subject of καθέζονται.

ὑπομνήματα δὲ ἐπὶ νίκαις Ὀλυμπικαῖς ἐστιν Ἱέρωνος τοῦ Δεινομένους τυραννήσαντος Συρακουσίων μετὰ τὸν ἀδελφὸν Γέλωνα.

Ἱέρωνος is the genitive subject of the copular predicate, with τοῦ Δεινομένους τυραννήσαντος Συρακουσίων as a genitive attributive/participial phrase; μετὰ τὸν ἀδελφὸν Γέλωνα means ‘after his brother Gelon’.

τὰ δὲ ἀναθήματα οὐχ Ἱέρων ἀπέστειλεν, ἀλλʼ ὁ μὲν ἀποδοὺς τῷ θεῷ Δεινομένης ἐστὶν ὁ Ἱέρωνος,

The first clause has τὰ ἀναθήματα as object of ἀπέστειλεν, with οὐχ negating the claim that Hiero sent them. In the adversative clause, ὁ ἀποδούς is a substantivized articular participle, subject of ἐστίν; Δεινομένης is the predicate genitive, and ὁ Ἱέρωνος is a genitival identifying phrase, literally 'the one of Hiero.'

ἔργα δὲ τὸ μὲν Ὀνάτα τοῦ Αἰγινήτου τὸ ἅρμα, Καλάμιδος δὲ οἱ ἵπποι τε οἱ ἑκατέρωθεν καὶ ἐπʼ αὐτῶν εἰσιν οἱ παῖδες.

Elliptical copular inventory: ἔργα is the topic, with τὸ μὲν ἅρμα and οἱ ἵπποι ... καὶ οἱ παῖδες as coordinated nominative subjects/predicative items; οἱ ἑκατέρωθεν modifies ἵπποι, and ἐπʼ αὐτῶν governs παῖδες. The exact attachment of the second οἱ and the scope of τε is somewhat uncertain.