Learn Swedish: Läs bilagan beträffande ditt nya lösenord. - Read the attachment concerning your new password.

It is a present participle (a verb form ending in -ande or -ende), formed from the verb att beträffa (to concern). However, in this sentence, it functions entirely as a formal preposition meaning concerning or regarding.

Could I use angående or gällande instead of beträffande in this sentence?

Absolutely. All three are present participles that double as formal prepositions of reference. Angående (regarding) or gällande (concerning or applying to) would mean exactly the same thing here, though beträffande can sometimes sound slightly more formal or bureaucratic.

Why does ny take the -a ending (nya) if lösenord is a singular ett-word?

Because it follows a possessive pronoun (ditt). In Swedish, possessives force the following adjective into the definite (weak) form, which usually ends in -a. Notice that the noun itself remains indefinite (lösenord, not lösenordet), which is the strict rule after possessive pronouns.

Is bilagan specifically an IT term for an email attachment?