Τῇ ἐπαύριον βλέπει τὸν Ἰησοῦν ἐρχόμενον πρὸς αὐτὸν
επαυριον is an adverb. Which of the adverbial questions does it answer? What verb is modified? What is the DO of βλεπει?
ερχομενον is anarthrous. Hence, it can be either adjectival or adverbial. Here, ερχομενον is attributive. It is modifying Ιησουν. Think of it this way, Jesus is the “coming to him” Jesus. When you put it like this, you can see the attributive nature of the participle more clearly.
καὶ λέγει· ἴδε ὁ ἀμνὸς τοῦ θεοῦ ὁ αἴρων τὴν ἁμαρτίαν τοῦ κόσμου.
Ιδε here is an interjection. It has no other connection to any other part of the sentence. This also explains why αμνος is is in the nominative case. You need not spend any time on this; but if you wish, you can see an explanation in GGBB p. 60.
θεου is probably an ablatival genitive. Use GGBB p. 72 to decide which category best fits the context here.
Check the participle memory forms to parse αιρων. αιρων is another attributive participle. Again, think of it as this Lamb is the “removing the sin of the world” Lamb (αμνος). Attributive participles are usually translated into English using an adjectival dependent clause. In this case, “The Lamb of God, Who removes…”
οὗτός ἐστιν ὑπὲρ οὗ ἐγὼ εἶπον·
Lexical form of ειπον is λεγω.
ὀπίσω μου ἔρχεται ἀνὴρ ὃς ἔμπροσθέν μου γέγονεν,What is the subject of ερχεται? What is the dependent clause? Which noun does the relative clause modify?
ὅτι πρῶτός μου ἦν.How did you translate οτι? Is this clause adverbial or adjectival?
κἀγὼ οὐκ ᾔδειν αὐτόν,
καγω is an interesting conglomeration of και and εγω.
ἀλλ᾽ ἵνα φανερωθῇ τῷ Ἰσραὴλ διὰ τοῦτο ἦλθον ἐγὼ ἐν ὕδατι βαπτίζων.
In your translation, you will probably put διὰ τοῦτο ἦλθον ἐγὼ ἐν ὕδατι βαπτίζων before ἵνα φανερωθῇ τῷ Ἰσραὴλ.How do you know that δια means “on account of” and not “through”?