"My grandfather loves me very much."
Translation:Mi abuelo me quiere mucho.
While "querer" literally means "to want," it also means "to love." You can express love for things, friends, girlfriend/boyfriend, spouses, family, etc. with "querer." You would only use "amar" with close family members, spouses, or in a deep and committed romantic relationship (such as fiancés).
You can say "mi abuelo me ama mucho," but it would also be appropriate and common to say "mi abuelo me quiere mucho."
Boyfriends and girlfriends typically say "te quiero mucho" to each other. Good friends say that to each other, too.
"Querer" does not imply sexual desire, however -- that could be expressed with "desear." For example, "te deseo" translates to "I want you."
It accepted "Mi abuelo me ama mucho." but rejected "Mi abuelo me ama muy mucho.". This seems inconsistent with many other exercises where "mucho" alone is translated to "a lot" and only "muy mucho" is translated to "very much"
As @JohnKTaylor says, those words don't work together the way they do in English (though you will sometimes see "mucho muy" used colloquially to emphasize the "very"). Spanish uses muchísimo to express "very much" to a stronger degree than mucho, which appears to be accepted as a valid response in this exercise.
"Muy mucho" is not grammatically correct. While it is true that "muy"="very" and "mucho"="much (or a lot)", they never go together.
They go together. "Used Occasionally. muy mucho is one of the 30000 most commonly used words in the Collins dictionary" https://www.collinsdictionary.com/us/dictionary/spanish-english/muy-mucho
Not necessarily. "Amar" is just a deeper level of sentiment reserved for very close relationships, while "querer" is used very broadly for any kind of relationship. See my comment elsewhere in this discussion.
Encantar isn't really used to express affection for people. It's mainly a stronger way of saying that you like a thing. Me gusta el fútbol, pero me encanta el béisbol. Quiero a mi tío, pero amo a mi mujer.
The object pronoun (me) goes right before the conjugated verb (me quiere). The a doesn't seem to be needed in this sentence.