Can أستاذة generally be used like سعيدة?
If you mean "سيّدة-Sayeeda" then generally speaking yes, you can use them interchangeably. Especially in the sentence above.
What you wrote "سعيدة-Sa3yeeda" means happy.
Shouldn't it be ِكَيْفَك?
In spoken language (especially in the Levant), you would not say it like how you wrote it. It would be spoken as either "kiifik (f)" or "kiifak (m)".
Change ma'am to match one of the Arabic Words
The Arabic word "ustadha" can be translated as "ma'am" or "professor (f)". It is perfectly fine the way it is.
ma'am usually maps to sayidati
Checkout Google translate and other sites like:
All of them point to sayidati
كَيْفَكَ يا أُسْتَاذٌ
وَ كَيْفَكِ يا أُستاذَةٌ
Is it true in Egypt they actually use مادام ?