Τῇ ἐπαύριον βλέπει τὸν Ἰησοῦν ἐρχόμενον πρὸς αὐτὸν
επαυριον is an adverb. ? ?
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.
Attributive participles are best translated into English using an adjectival dependent clause. In this case, “The next day, he sees Jesus who was coming to him.”
|stem||connecting vowel||participle morpheme||case ending|
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
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·
In your translation, you will need to provide a PN for the verb εστιν. “This is [the One] on behalf of whom…”
ου εγω ειπον is a dependent clause. Here, however, it is not adjectival or adverbial but a noun clause. It is the OP of υπερ.
Lexical form of ειπον is λεγω.
ὀπίσω μου ἔρχεται ἀνὴρ ὃς ἔμπροσθέν μου γέγονεν,
οπισω is an adverb here used as a preposition.
? ? ?
ὅτι πρῶτός μου ἦν.? ?
πρωτος is a superlative adjective here used as a comparative (GGBB p. 303).
κἀγὼ οὐκ ᾔδειν αὐτόν,
καγω is an interesting conglomeration of και and εγω.
ηδειν is a pluperfect form; first person, singular.
ἀλλ᾽ ἵνα φανερωθῇ τῷ Ἰσραὴλ διὰ τοῦτο ἦλθον ἐγὼ ἐν ὕδατι βαπτίζων.
ινα φανερωθη τω Ισραηλ is a dependent clause. The DMW indicates an adverbial function. The clause is answering the why? question. ?
In your translation, you will probably put διὰ τοῦτο ἦλθον ἐγὼ ἐν ὕδατι βαπτίζων before ἵνα φανερωθῇ τῷ Ἰσραὴλ.
βαπτιζων is anarthrous. This leads us to think it might be an adverbial participle. Recall that one of the adverbial questions is “how?”. Now ask yourself, how did he come? He came baptizing.
φανεροθη tense formative
φανερωθη principle 12
φανερωθη verb ending (there is none for 3rd sing.)