A shailah is a question requesting a religious ruling. You are usually asking your own LOR (local orthodox rabbi).
Here are some examples:
- Do I need to kasher a can opener? And if so, how?
- Can I scoop cat litter on Shabbat? Probably not, so can I just throw out all the litter to avoid separating bad from good?
- Should I report a co-worker who has admitted a violation of company policy to me in confidence?
- Should my child with a disability attend a school other than the local yeshiva?
- X has happened. Am I niddah?
- Are my children allowed to play with legos on Shabbat?
- Can I brush my teeth on Shabbat?
- Is Bailey's Irish Creme kosher?
Machlokes (also pronounced machloikes) is when the answer to that question is disputed. You know the old cliche, 2 Jews = 3 opinions. Or in stereotypical lawyerspeak, "It depends." Just about every shailah can be a machlokes.
For instance, I learned from a Twitter debate between rabbis that the lego question above is a machlokes. Whodathunkit?