there is no difference in English between masculine and feminine "teacher", however in Russian you can build correct sentence based on the first word which means gender:
Мой учитель - masculine
Моя учительница - feminine
For thouse who familiar with German, gender mistake is similar to something if I would say German: Die Apfel (for those who don't know German, Apfel (apple) is masculine and Die is The used with feminine). Hope this helps
You are correct that учитель is a word that belongs to the masculine gender. The person it refers to can, however, be female. This use is quite formal, though: in speech you'd rather use учительница when talking about one female teacher at a school (but her job is still called «учитель» or «преподаватель»).
Another native speaker (olimo) said in a different discussion that the female equivalent of "врач" (which I do not remember at all, maybe врачишка?) gives a connotation of disrespect, or a negative connotation in general, like implying a bad / non-serious doctor; and he said he would never refer to a female doctor that he respected by other term than врач.
Does this apply to учитель also, and more generally, to all or most professions?
No. (Учительница is a neutral or even positive word, though I'm sure that officially it is called учитель). There are very few officially feminine profession names in russian. Медсестра (m медбрат), швея, домохозяйка. The endings are from another story. -ница, -иса (директриса), -ка (санитарка) are neutral. -шка, -чка are positive (санитарочка) or negative (докторишка as you said).
-тель behaves similar to "-er". It takes a verb and makes a noun that means someone/something doing the action.
For example, читатель is the one who reads, учитель is the one who teaches, создатель is the one who creates, родитель is a parent (bear-er), and выключатель is a switch (turn-off-er).
For better or worse, typos are recognised automatically. For languages like French, German, or English your answer is accepted if a word is 1 character away from the correct word, or 1 swap away— unless the result is a different word.
For example, "itme" or "toime" are "time" typed incorrectly. On the other hand, "tide", "tie" or "times" will be counted as a mistake.
The system does not always work in languages exclusively taught in volunteer-created courses (they do not have a dictionary and a language model).