I have been wondering. Does one need to be gifted
To read the tarot accurately?
Everyone is gifted in many ways but not all people are gifted with reading cards or having strong psychic abilities. Learning to recognize and having the courage to use our gifts is the key. Even those of us who have strong intuitive (psychic I believe) gifts need to learn card meanings and interactions among groups of cards plus we have to cultivate the ability to "hear" the message given by the cards above and beyond just reciting rote card meanings. I don't believe one has to consider themselves gifted to read the cards. Many, many people here who read cards phenomenally well don't consider themselves to necessarily have a gift.
Is it possible that someone could be good at picking cards but not at interpreting them while someone could not be intuitive at picking cards but good at interpreting?
A good reader is a good reader, whether they draw the cards themselves or not. I'm not sure I'm understanding this question but I don't believe there's such a thing as someone who can read the cards well but doesn't choose the cards well and vice versa.
What makes a good reader? Is it possible that someone who is very accurate for another person is not accurate for you?
Although I have a pretty good track record with giving readings that are relevant to what's going on in the sitter's life, I don't aim to be accurate. I aim to be helpful and to find the message the cards mean to give to the sitter without personal bias. I say "I aim to" but that doesn't mean I'm always successful.
I can be pretty biased---or come across that way---so every once in awhile I get called on that. Not within my readings but just in general. In my readings I try to "just stick to the facts, ma'am" like that old TV show detective used to say.
ETA: I forgot to answer one of your questions here---yes, it's entirely possible that what one reader sees in your cards "accurately", another reader won't, but most readers see similar things in each spread, even if they're different cards. The message is often essentially the same. However, it's my belief that as readers, we only see in the cards what we're given to see. Sometimes we're not the one who is supposed to carry a certain message for that sitter and in that case, then we won't see it in the cards.
As far as the cards go, they basically "pick" themselves, so I work on interpretive skills.
Barleywine's whole post was good, but this first sentence of his sums it up for me, too. No matter who picks the cards, they're the cards that are meant to come up for that spread and my job as a reader is to be able to read the cards as truly as possible so I can give my sitter the most appropriate answer based on those cards.
Most of us who have read cards for years are still embarked on a never-ending education. I feel safe in saying that for others here and certainly for myself. For me, there never comes a time when I say, "Well, that's that. Now I know all I need to know."