Meaning please

Great questions, Sanjay.  Your questions keep us on our toes!

One of the expressions you've asked about is quite formal, and the other is quite casual.

Kindly is a quite formal adverb that either (1) has the same meaning as please. In formal situations, it is used to make a request sound more polite (Would you kindly remove your shoes?) or (2) only together with the verb take, and, I think, almost always if not always following a negative main verb, has the same meaning as react favorably.  Patty's sentence means that "we don't react favorably to commands." In other words, we are not happy when we are given commands.

Cave to [something] means to surrender, submit or yield to something.  It is quite informal, and is probably only appropriate in spoken English or casual written contexts.  When I wrote that I would cave to the use of subterfuge as a plural countable noun, subterfuges, I meant that my preliminary opinion was that subterfuge should be uncountable, but if Erle Stanley Gardner, and especially Patty T., thought the plural countable form was correct, I would submit to (agree with) their opinion on the matter.

I hope this helps.

Shawn

PS - to keep [someone] on [his/her/their, etc.] toes is an idiom that means that someone causes someone else to be alert and prepared.  You ask a lot of great, and sometimes difficult, questions on Grammarly.com, which makes those of us who answer such questions alert and ready.  If we didn't have you, and didn't have to respond to your great questions, we might get lazy, but because of your queries we are on our toes, ready to answer many different kinds of questions.  Perhaps the origin of this idiom relates to ballet, but I am not entirely sure about that.