普段 and 通常: everyday habits and normal operation
Compare everyday personal habits with normal operating conditions.
Everyday life and habits
普段 is read ふだん and refers to ordinary, nonspecial occasions. 「普段は電車で通っています」 describes usually commuting by train.
「今日は普段より早く起きました」 means that the speaker got up earlier than usual today. The comparison is with their own routine, not a standard time for everyone.
Normal operation and conditions
通常 is read つうじょう and refers to normal conditions or procedures rather than exceptions. 「明日は通常どおり営業します」 announces that the business will operate as usual tomorrow.
「通常は三日かかります」 explains that it normally takes three days. It is not a guarantee without exceptions, so do not expand it into a promise of completion within three days.
Considering register and reference points
Both 「普段どおり」 and 「通常どおり」 can mean 'as usual.' 通常 tends to fit business notices and procedural explanations, while 普段 fits everyday personal accounts.
These tendencies do not strictly restrict their subjects. Rather than assuming 普段 is impossible in formal settings, check what counts as usual and what register the notice uses.
Does 「通常より時間がかかります」 mean that it will finish faster than usual?
Show the answer and why
No. It means that it takes longer than normal. The comparison indicates increased time, not faster completion.