Brasidas, not Brasidus. He’s a Spartan, consistently with the Doric ending of his name, -ίδας not –ίδης.
I’ll comment on the trickiest part of this, οὐκ ἂν ἡγεῖτο μᾶλλον περιγενέσθαι ἢ ἄνευ προόψεώς τε αὐτῶν καὶ μὴ ἀπὸ τοῦ ὄντος καταφρονήσεως.
ἡγεῖτο is “he thought”—it’s not passive.
The αν (as well as the negative) applies not to ηγειτο but to περιγενεσθαι, so it’s not “he’d not be thinking that he came out on top,” as it looks to be, but “he thought that he wouldn’t come out on top.” (περιγενεσθαι represents aor.optative.) This is regular Greek idiom. Cf. the last line of the piece, οὐκ ἂν νομίζων αὐτοὺς ὁμοίως ἀπολαβεῖν …, where you rightly attached the ουκ αν to απολαβειν (again representing aor.opt.).
μᾶλλον περιγενέσθαι ἢ ἄνευ προόψεώς τε αὐτῶν καὶ μὴ ἀπὸ τοῦ ὄντος καταφρονήσεως is where it gets tricky. Brasidas thinks he has a better chance of surviving/succeeding if the Athenians&allies don’t get an advance look (προοψις) at his forces. He wants to fool them into thinking that his forces are stronger than they really are. If they realized how inferior his forces are they’d be contemptuous of them and wouldn’t hesitate to take them on. Thuc. expresses himself very harshly here. Usually his narrative is reasonably straightforward, unlike his speeches, but this is an exceptionally knotty sentence, Thucydides at his most rebarbative. You have to really wrestle with it.
Lit. “He thought he wouldn’t rather [i.e. be more likely to] succeed than without prior sight of them and not from contempt for the actuality [του οντος; i.e. the inferiority of his forces].” That’s to say (I think!), he thought he’d be more likely to succeed if [the enemy] didn’t see them ahead of time and [thus] feel contempt for their actual strength [which is weaker than B wants the enemy to believe].
Other details:
(ἀντίπαλα γάρ πως ἦν) “for they were (just about) evenly matched” (numerically).
οὐκ ἂν νομίζων αὐτοὺς ὁμοίως ἀπολαβεῖν αὖθις μεμονωμένους
The subject of απολαβειν is the same as the subject of νομιζων, i.e. Brasidas; αυτους is object. “thinking that he wouldn’t catch them (cut them off) similarly isolated a second time”
εἰ τύχοι ἐλθοῦσα αὐτοῖς ἡ βοήθεια. ει is just “if”: “if reinforcements came”; he wouldn’t get another chance “if they happened to get (succeeded in getting) help.” αυτοις is the Athenians&allies, like αυτους above.
The rest is pretty good. I think you are improving.