Welcome to the Grammar Exchange, and thank you for your question. I'm sorry it has taken me so long to respond to this thread.
I also want to thank Tony for his valuable input.
Cailin, when you have numerous examples that you want us to examine in contrast, please use index numbers or letters to make it easier for us to refer back to them. For example:
a: I remember buying bread
b: I remembered to buy bread
Also, it helps if your pairs of examples are parallel constructs. Hence, to be a good comparison with (b), it would help if the verb in (a) were in the same tense:
a': I remembered buying bread.
Here, it's so easy to add a prime symbol (which is essentially an apostrophe) to make it clear that I am making a slight variation on your original example (a) as opposed to creating a whole new example of my own.
Again, I wish to thank Tony. He has given excellent answers to all of your questions. The only difference between (a) and (a') is that in (a), the remembering of the past event of buying is happening now, but in (a'), the remembering happened in the past, and the buying happened even earlier.
Your "forget/forgot" examples follow a similar pattern, but your "regret" examples are perfect, in that both examples are in the simple present, but, as Tony shows us, the difference between using the gerund as opposed to the infinitive changes the meaning entirely.
This doesn't work with all verbs, though. These two sentences essentially mean the exact same thing:
i: She hates changing her baby's diaper.
j: She hates to change her baby's diaper.
Cailin, what makes your last example especially confusing is the apparently unnecessary introduction of a negation in addition to changing the tense and mood of the verb. Can't we keep it more simple?
g: She stopped buying food.
h: She stopped to buy food.
As Tony says, (h) (oh, man alive, it is so nice to have a simple index letter by which to refer to this sentence) means she ceased to do one action (probably driving or walking) in order to do another, which, in this case, is entering a store in order to buy food.
On the other hand, (g) means either that she is on a hunger strike, or has become a thief.