I think what is going on in your examples is that you are confusing gerunds with verbs (gerunds are words that are derived from verbs but function as nouns). As such, they do not have properties of verbs, including tense. Walking is not the present tense of "walk" because "walking" is the thing that someone does when performs the verb "to walk".
Your two examples are both very run on sentence that. While not a hard rule, you should only have one verb per sentence, unless both verbs happen at the same time.
In your first example, the following verbs can be broken into separate sentences (bold):
She took one step before the brass bell above her door echoed a sharp chime through her senses and she snapped to, standing up straight and pushing her scraggly long black hair to the side of her face, before mustering a smile toward the individual standing outside her window.
There's a few additional sentences that could probably broken out of this that lack verbal words (after "snapped" there are several actions that are implied to happen at the same time. You have a good paragraph of events that should happen in an ordered sequence (even if the time is minute between them, she "snapped to" in reaction to the bell chime, not at the same time as the bell chime, and you clearly say that she took a single step before the bell made a sound, not at the same time as it sounded).
Since you brought it up in your post, the tense does not change in dialog either as all dialog is quoted by the narrative voice (the entity telling the story to the reader. In third person, the narrator may be thought of as a separate character who is typically in capable of interacting with the characters of the story. If you've ever seen the film "The Muppet's Christmas Carol", the film casts Gonzo as "Charles Dickens" who is telling the story to the audience. Much of his dialog comes from the narrative voice from the book the film is adapting (and gives the film a notoriety of one of the best adaptations of the book by fans of Charles Dickens).
In a dialog, when the following occurs, note the bolded verb and the italicized verbs:
"If they would rather die, then they had better do it and decrease the surplus population," Scrooge shouted.
This is all one sentence with the single verb of the sentence, being "shouted". Now, all the italicized words are verbs, but the quote in its entirety is the noun that Scrooge shouted. Scrooge shouted it in a tense (and voice for that matter) that was consistent with the conversation it is a part of, and not consistent with the conversation, but would be consistent with a narrative voice, if it wasn't a direct quote.
Go back to the idea of Gonzo/Charles Dickens/Narrator idea. In written word, because we do not have actors, the narrator is traditionally the sole teller of the story to the reader, thus will be in a consistent voice (to get an idea, listen to the U.S. audiobooks of Harry Potter, where the the person who reads the books, Jim Dale, uses a distinct voice for each character's spoken dialog as well as a unique voice for the non-dialog narrative (it's very similar to Harry's dialog voice, but he changes it just enough that it's noticeable).
Quotes should replicate exactly what was said, warts and all, and as such are permitted to reasonably violate grammar rules where non-quoted portions of written texts are not. Grammatically correct spoken English is not realistic.