Jag minns mitt lösenord men inte mitt användarnamn.

Because lösenord and användarnamn are both ett nouns in Swedish.

Swedish possessives change form like this:

• min for singular en words
• mitt for singular ett words
• mina for plurals

So:

• min bok = my book
• mitt lösenord = my password
• mitt användarnamn = my username
• mina böcker = my books

Since both nouns here are singular ett nouns, mitt is correct both times.

Because in Swedish, a possessive usually replaces the article.

So you say:

• mitt lösenord
• mitt användarnamn

not:

• mitt ett lösenord
• mitt ett användarnamn

This is similar to English: you say my password, not my a password.

Minns is the present tense of the verb minnas, which means to remember.

Examples:

• jag minns = I remember
• du minns = you remember
• vi minns = we remember

In the present tense, Swedish verbs do not change according to person, so the verb form stays the same.

Related forms:

• infinitive: minnas
• present: minns
• past: mindes

Yes. That is very common.

You can say:

• Jag minns mitt lösenord
• Jag kommer ihåg mitt lösenord

Both mean I remember my password.

A rough difference:

• minnas / minns can sound a little more compact or slightly more formal in some contexts
• komma ihåg is extremely common in everyday speech

Both are natural Swedish.

Because Swedish often leaves out repeated words when they are easy to understand from the context.

The full version would be:

• Jag minns mitt lösenord men jag minns inte mitt användarnamn.

But Swedish commonly shortens this to:

• Jag minns mitt lösenord men inte mitt användarnamn.

This kind of omission is very natural, especially after words like men and och.

In the full clause, inte comes after the finite verb:

• Jag minns inte mitt användarnamn.

In your sentence, the second jag minns is omitted:

• Jag minns mitt lösenord men inte mitt användarnamn.

So inte is still understood as negating the missing verb phrase. In other words, it really means:

• ... men jag minns inte mitt användarnamn.

So the placement is completely normal once you understand that the verb has been left out.

Because Swedish normally writes compound nouns as a single word.

So:

• lösen + ord = lösenord
• användar + namn = användarnamn

This is very typical in Swedish. English often writes similar expressions as two words, but Swedish usually joins them.

More examples:

• mobiltelefon = mobile phone
• sjukhus = hospital
• vardagsrum = living room

A useful clue is the last part of the compound.

In Swedish, compound nouns usually take the gender of the final element:

• namn is an ett noun
• ord is an ett noun

So:

• användarnamn is an ett noun
• lösenord is an ett noun

That is why you get:

• ett användarnamn
• ett lösenord
• mitt användarnamn
• mitt lösenord

Yes, absolutely.

Full version:

• Jag minns mitt lösenord men jag minns inte mitt användarnamn.

Shortened version:

• Jag minns mitt lösenord men inte mitt användarnamn.

The shortened version is more natural in everyday language because it avoids repetition. The full version is still correct, but it sounds a little heavier.

In careful pronunciation, jag is often pronounced something like yahg.

But in everyday spoken Swedish, it is very often reduced, and may sound more like:

• ya
• ja

depending on dialect and speaking style.

So learners often hear something closer to:

• Ya minns mitt lösenord ...

That is normal spoken Swedish.