Ég ruglast stundum á beygingunni þegar ég skrifa í þátíð.

Because að ruglast and að rugla are related but not the same.

Að rugla usually means to confuse something, mix something up, or muddle something.

Að ruglast means to get confused yourself, to become mixed up, or to make a mistake.

So in this sentence, the speaker is not saying that they confuse something else. They are saying that they themselves get confused. That is why ruglast is the natural form here.

The -st ending is a very common Icelandic pattern, often called the middle voice. It can give a verb a reflexive, passive-like, or intransitive meaning.

In a sentence like this, ruglast has the sense of getting confused or mixing things up oneself.

So:

að rugla = to confuse, mix up
að ruglast = to get confused, to mix things up

You will see this pattern in many other Icelandic verbs too, so it is worth getting used to.

Here á is just the preposition that goes with this expression. The phrase að ruglast á einhverju means to get confused about something or to mix one thing up with another.

It does not translate neatly as English on. You should learn it as a full pattern:

ruglast á + dative

For example:

Ég ruglast á þessum tveimur orðum.
I mix up these two words.

So in your sentence, á beygingunni is part of that same pattern.

Because á takes the dative here, and the noun is also in the definite form.

The base noun is beyging, meaning inflection or grammatical change of form.

Very roughly, the pieces are:

beyging = inflection
beygingu = dative singular
beygingunni = dative singular definite, meaning the inflection

So á beygingunni means something like about the inflection or with the inflection, depending on how naturally you translate it.

Because Icelandic often uses the definite form when the thing being talked about is understood from context.

Here the speaker means a specific thing: the relevant inflection pattern they are dealing with while writing. So beygingunni sounds natural as the inflection or the word-form pattern.

English does not always use the in the same places Icelandic does, so this is something learners often need to get used to.

Beyging is a general grammar word meaning inflection. It covers the way words change form.

Depending on context, it can refer to things like:

noun declension
verb conjugation
adjective inflection

In this sentence, it means the grammatical forms or endings the speaker has to choose when writing in the past tense. So it is broader than just one English grammar label.

Because the sentence is talking about a habitual situation, not about one single event in the past.

The meaning is basically:

I sometimes get confused with the inflection when I write in the past tense.

That is a general truth about what happens to the speaker from time to time, so the main verb and the verb in the þegar clause are both in the present.

English does the same thing:

I sometimes get confused when I write in the past tense.

Even though past tense is mentioned, the sentence itself is still about a present, repeated habit.

Yes, í þátíð is the normal expression for in the past tense.

It refers to using past-tense verb forms. So here skrifa í þátíð means to write using the past tense, not necessarily to write about something that happened in the past in a loose, general way.

It is a good idea to learn í þátíð as a set phrase.

Because þegar introduces a subordinate clause.

In Icelandic main clauses, the verb often comes early because of the usual verb-second pattern. But subordinate clauses do not work the same way. After þegar, the normal order is:

þegar + subject + verb

So:

þegar ég skrifa

is the expected word order.

That is one of the differences between main-clause and subordinate-clause syntax in Icelandic.

Yes. Stundum is fairly flexible.

Your sentence has a very natural neutral order:

Ég ruglast stundum á beygingunni þegar ég skrifa í þátíð.

But you could also say:

Stundum ruglast ég á beygingunni þegar ég skrifa í þátíð.

That version puts a little more emphasis on sometimes.

So the meaning stays very similar, but the focus and rhythm change slightly.

Þ is pronounced like the English th in thing.

So:

þegar starts with the same type of sound as think
þátíð does too

It is never pronounced like the th in this. That voiced sound is normally written with ð in Icelandic, not þ.

For an English speaker, that is one of the most useful pronunciation distinctions to learn early.