You can say:
I will go home shortly.You can also say:
or
I will go home soon.
I am asleep by ten o'clock on weekdays.
or
I am asleep by ten on weekdays.
or
I am asleep by ten on weekdays.
or
I am asleep by ten on Saturdays.
I think you're asking the wrong questions - that is, one question does not correlate with the other.
If you ask a student to write a sentence with "currently" in it, and they write:
"I'm going home currently", and someone says that's not a good English sentence because you should use "now" not "currently", then the question "What is the correct form of that sentence" is the wrong question.
There is nothing wrong with the form of the sentence. It's just the wrong sentence for "currently".
He is currently a student at RPI.
I am currently in my car on my way home.
She is currently single, so if you know any interesting single men, send them her way.
It describes the state of the person NOW, or what that person is doing NOW.
Sleep is an ongoing activity. You 'go to sleep' or you 'fall asleep' at 10pm. You sleep from 10pm to 6am.
'Sleep' as a verb does not mean 'go to sleep'.
Other languages have different verbs for 'sleep' and 'falling asleep'. For example in Italian, dormire means to sleep; addormentarsi means 'to fall asleep'. English does not have a separate verb, but you still can't use 'sleep' for 'going to sleep'.
The same applies to 'work'
I work at 9am every morning. - Wrong
'Work' as a verb does not mean 'start working'. You start work at 9am, or you 'start to work' or you 'start working'.