Grandma is in Genitive singular. This can be confusing for beginners because 2/3/4 Grandmas are all Genitive Singular in Russian. For example: Эти две бабушки гуляют. You know that there are two grandmas are walking, but бабугки is in Genitive Singular in this sentence.
You will get used to this with more exposure in Russian. You will know that when a Russian says, "суп твоей бабушки" It is one grandma because of the context of the sentence.
"Dogs" ends in "s" when plurilized thus "many" can be used to describe a large quantity of these dogs, but "a lot" (as far as my understanding goes) is reserved for those nouns that do not end in "s" when plurilized, such as "water", "air", "deer", but I suppose my English professors could be wrong.