You know I'm going to the park tomorrow?
This is really "Do you know [that] I'm going to the park tomorrow?" with the initial do being subject to "conversational elision" which can happen when speakers are familiar with each other.
You know how I'm going to the park tomorrow?
"You know how X" is basically shorthand for "Recall X (X is something I expect you to have heard before or know about), because I'm about to tell you something interesting pertaining to X that will change X."
A: You know how John always comes in late?
B: Yeah ... did something happen?
A: Yep. Well today, the boss was waiting for him, and took him in the office.
B: Uh-oh. I wonder if he is getting fired.
So these two express very different things. One is asking a question and the other is preparing the listener for further information.
Well, my boss and I were supposed to take them out to dinner on Wednesday night.
This happened last night. The past tense is obviously needed here.
But this morning, she walks into my office and tells me she can’t make
it after all.
Simple present tense is often used to narrate or describe actions that are happening. It has a "disconnecting" effect - as though someone external to the activity is observing that activity. This applies even if used in the first person.
Present progressive is normally used if you don't want this "disconnecting" effect.
I'm walking to the park
This is the typical way to express that you are walking in the present.
I walk to the park
Hard to explain - but it sounds like there's a separate entity from yourself that is saying this. Even though the verb is in the first person. As though you are watching yourself walk to the park and stating that fact in observation. This concept fits perfectly if you are recounting events that just happened.
Simple present in the third-person sounds a lot less weird and is much more usual.