Learn Hardcore Finnish: En halua asioida verkossa tänään, koska netti on jumissa. - I don’t want to take care of things online today, because the internet is stuck.

Yes. asioida is the first infinitive (the dictionary form), meaning to do errands / to deal with matters / to conduct business.
In haluan / en halua + infinitive, Finnish works like English want to + verb:

en halua asioida = I don’t want to do errands / handle things

Does asioida verkossa literally mean “to do errands online”? Is that idiomatic Finnish?

Yes, it’s idiomatic. asioida verkossa means doing practical tasks online (banking, filling forms, using e-services, shopping for necessities, etc.).
Common alternatives you may also see:

hoitaa asioita verkossa = handle things online (very common)
asioida netissä = same meaning, slightly more casual because netissä is more colloquial than verkossa

Why is verkossa used here? What case is it?

verkossa is the inessive case (-ssa/-ssä), meaning in something:

verkko = network / web
verkossa = in the web / online

Finnish often expresses “online” as being “in the web/network.”

Can I say netissä instead of verkossa? Is there a difference?

Yes, you usually can:

verkossa = slightly more neutral/formal
netissä = more everyday/colloquial

Both mean “online” in this context.

Where can tänään go in the sentence? Is the word order fixed?

It’s flexible. tänään (today) can move depending on emphasis:

En halua asioida verkossa tänään... (neutral)
En halua tänään asioida verkossa... (emphasis on today, e.g., “not today”)
Tänään en halua asioida verkossa... (strong “today” topic)

Finnish word order is often used for focus rather than grammar constraints.

Why is it koska? Could I use something else for “because”?

koska is the most common, neutral “because.” Alternatives include:

sillä = “for / because” (often more written-style; typically links two main clauses)
kun can sometimes mean “because” in Finnish, but it often means “when,” so learners should be cautious.

Your sentence uses koska naturally for a clear reason/explanation.

Why does the second part say netti on jumissa and not something like “the internet is stuck”?

That is exactly what it means—Finnish just says it in a very everyday way:

netti = the internet (casual)
on jumissa = is stuck / jammed / not working / frozen

So netti on jumissa is a common spoken-style way to say the internet connection is not functioning.

What does jumissa mean grammatically? What case is it?

jumissa comes from the noun/adjective-like word jumi (“jam/stuck state”) and is used in the inessive (-ssa) to describe being “in a jam/stuck.”
This is a common Finnish pattern for “state/condition” expressions:

olla jumissa = to be stuck
olla hukassa = to be lost
olla paniikissa = to be in a panic

So on jumissa functions like “is stuck.”

Could I say Internet on jumissa or verkkoyhteys on jumissa instead of netti?

Yes, with slight differences in register/precision:

netti on jumissa = most casual, very common
internet on jumissa = also fine, still fairly casual
verkkoyhteys on jumissa = “the network connection is stuck/down” (more specific/technical)

Why isn’t minä written? How do I know it’s “I”?

Finnish often drops subject pronouns because the verb form (or here, the negative verb) shows the person:

en already marks 1st person singular, so minä is optional.

You might add minä for contrast/emphasis:

Minä en halua asioida verkossa tänään... = “I don’t want to…” (implying someone else might)

How would this change in the past tense: “I didn’t want to do things online today, because the internet was stuck”?

One natural version is:

En halunnut asioida verkossa tänään, koska netti oli jumissa.

Notes:

Negative verb stays en (present form), but the main verb becomes past participle-like: halunnut
on (present “is”) becomes oli (“was”) in the reason clause.