知る and 分かる: know information or understand it
Separate coming to know something from the resulting state of knowing it, then compare both with understanding a meaning or situation. Learn 知っている and 知らない as a pair.
The time difference between 知る and 知っている
知る can mark the change of acquiring new information. ニュースでその事実を知りました。 says that the person learned that fact through the news, and the newly learned fact takes を.
Use 知っています for the resulting state of already having knowledge. あの店を知っています。 means that someone knows of that shop or has information about it. Do not use 知ります as the ordinary way to say “I know it now.”
The basic negative and the pattern of 分かる
When 知っていますか。 is answered negatively, the ordinary response is いいえ、知りません。 or the conversational 知らないです. Do not mechanically negate the surface form and treat 知っていません as the default answer in every situation.
分かる focuses on understanding or identifying a meaning, reason, method, or situation. この説明がよく分かります。 and 答えが分かりました。 commonly mark what is understood or worked out with が.
Different focus even with related information
その店を知っています。 says that you know of the shop. その店の場所が分かります。 says that you know or can identify where it is. Choose between general knowledge and specific understanding according to the context.
言葉の意味を知っていても、使い方が分からないことがあります。 shows that knowing a word’s meaning does not guarantee understanding how it is used. 分かりました can acknowledge that an explanation was understood, while 知りました is not used as the same routine acknowledgment.
Quick check: What is the usual negative reply to その人を知っていますか when you do not know the person?
Show the answer and why
Answer いいえ、知りません。 Although the question uses the state 知っています, the ordinary negative reply uses 知りません rather than treating 知っていません as the default.