Learn Hardcore Russian: Я подошёл к окну и увидел, что на улице идёт град. - I walked up to the window and saw that it was hailing outside.

Подошёл is past tense, masculine, perfective: it presents the action as completed—I came up (and arrived) at the window.
Подходил (imperfective) would usually mean something like I was walking up / I used to come up, focusing on the process or repetition, not the completed arrival. In this sentence, the completed arrival naturally sets up the next completed event (увидел).

Why do both verbs appear in the past tense (подошёл and увидел)?

Because the narrator is describing a finished sequence of events in the past: first I approached, then I saw. Russian commonly uses a chain of past perfective verbs to show successive completed actions.

What does к mean here, and why is it к окну?

к means toward / up to and requires the dative case.
окно → dative singular окну. So подойти к окну = to come up to the window (motion toward a destination).

Why is it окну (dative) and not окна (genitive) or окне (prepositional)?

Different prepositions require different cases:

к окну (dative) = movement toward the window
у окна (genitive) = being by/near the window (location)
в/на окне (prepositional after в/на) = being in/on the window area (less common depending on meaning)
Here we need movement toward it, so к + dative.

Could I say Я подошёл к окну и увидел град without что?

Not with the same meaning/structure. увидел, что ... introduces a whole clause: I saw that ... (I realized/observed a fact).
If you say увидел град, that means you directly saw the hail itself (as an object): I saw hail. That’s possible, but it’s slightly different from I saw that it was hailing outside.

Why is there a comma before что?

Because что introduces a subordinate clause (что на улице идёт град). In Russian, subordinate clauses are normally separated by commas from the main clause: увидел, что ....

Why does Russian use идёт with hail? It literally means goes, right?

Yes, идти literally means to go, but Russian uses it idiomatically for many kinds of precipitation:

идёт дождь = it’s raining
идёт снег = it’s snowing
идёт град = it’s hailing
It’s like the rain is coming down / it’s going on—a standard weather expression.

Why is идёт present tense if the whole story is in the past?

Because the narrator approached the window in the past and at that moment observed a situation that was true then: it is (was) hailing outside.
Russian often keeps the weather clause in the present when describing what someone sees at that moment, especially with увидел, что .... You can also use past (шёл град) to emphasize that the hailing was occurring at that time in the past; both can work depending on style and context.

What’s the difference between град and градус? They look similar.

They’re unrelated words:

град = hail (the weather phenomenon)
градус = degree (temperature/angle)
Also, град can appear in place names/old words meaning town, but in this sentence it’s clearly hail.

Why is it на улице, not в улице?

Russian typically says на улице to mean outside / out in the street / outdoors.
в улице is generally not used for “outside”; в would mean “inside something,” and a street isn’t treated as an “inside” space in this expression.

What does the word order add here? Could it be rearranged?

Yes, Russian word order is flexible, but it affects emphasis.

Я подошёл к окну и увидел, что на улице идёт град. = neutral narration
Я подошёл к окну и увидел, что идёт град на улице. = more focus on град (hail)
К окну я подошёл и увидел... = emphasis on the action/location to the window (more literary)
The original is the most straightforward.

Why are the verbs masculine (подошёл, увидел)? What if the speaker is female?

Past tense in Russian agrees in gender and number with the subject:

masculine singular: подошёл, увидел
feminine singular: подошла, увидела
plural: подошли, увидели
So a female speaker would say: Я подошла к окну и увидела, что на улице идёт град.