KAYFABE: Andre did get the occasional World Title shot (not just WWF) but always won by DQ or countout, so he never actually won the title. The Champs really didn't want to defend against Andre because of Andre's size and skills, so they always managed to get DQ-ed or counted out. To the best of my knowledge, Andre didn't challenge face Champs, only heels (before turning heel on Hogan).
Andre wasn't really undefeated for 15 years in a row; that was just a marketing ploy by the WWF. But he did only lose a couple of times (fairly) in those 15 years. And went 60 minutes to time limit draws with Harley Race and Nick Bockwinkel.
Andre didn't stay in any particular promotion long enough to establish himself as a contender for championships. He moved around constantly, wrestling all over the world for whoever he wanted. His spot on the card as "special attraction" generally took top billing and was the main event. It could be argued that Andre being on the card was more important, and was a bigger draw, than even the World Champ. Really, Andre was World Champ in everything but name only. He got the money and perks the World Champs got, was billed as "special attraction" and got the main events. He didn't need a World Title.
NON-KAYFABE: Andre was over 7 feet tall and about 500 pounds, and he could move very well for such a gigantic man. Nowhere would it have been believable that a 230-250 pound normal-size man could out-wrestle and pin the Giant. I've written here many times that Andre could wrestle, do drop-kicks, and even run, but I wrote that to illustrate the difference between Andre in his prime and the pain-racked nearly-crippled Andre his last few years as a heel in the WWF, NOT to claim that Andre could wrestle like Bret Hart. I wrote that to counteract the sad comments I read from fans who DON'T know Andre claiming Andre was a "washed-up has-been". In his prime, nobody could beat Andre. Nobody. He only lost when HE wanted to, to further a feud or angle. Nobody could shoot on him and actually beat him. Andre would have crushed anybody who tried.
So putting any World Title on Andre would have meant Andre being World Champ for as long as he wanted because nobody COULD beat him. Not that Andre would have hijacked the title and kept it forever, but that it wouldn't be believable for a normal-size wrestler to beat him.
Andre was "the eighth wonder of the world", the most popular wrestler in the world in the 70's and early 80's (until Hogan exploded world-wide), a "special attraction" who sold out arenas anywhere in the world he wrestled. He didn't need any championship to make him more famous than he already was. Plus, Andre enjoyed the freedom of being able to wrestle when and where HE wanted. A championship would have put a stop to that as he would have to wrestle according to the promotion's schedule.
1: From 1970 (when he debuted in Japan) through 1981 (his feud with Killer Khan). After that, the disease that made him a giant started really affecting his body and his health. His weight ballooned up and his mobility steadily decreased.
2. His "look" and the way he was presented by promoters all over the world. He looked like a fairy tale giant, a monster, but was really a "gentle giant" and very friendly. He was presented AS a giant who couldn't be beaten, and he made his reputation winning battle royals all over the world. Other giants like Big Show and Khali are just presented as bigger-size "normal" wrestlers, who win and lose just like everybody else.
3. Hell no! The WWE has a well-earned reputation for regularly screwing up good things. They'd make Andre no different from The Big Show, Khali, and every other big guy. It was Vince SENIOR, more than any other promoter, who made Andre into the "eighth wonder of the world", the unbeatable giant. It was Vince JUNIOR who turned him into a "jobber to the stars" to get Hogan and the Warrior over.
4. He'd be at the same level as The Big Show, I think.
5. How many times has Big Show been World Champ? Andre would have about the same amount. It should be noted that Andre liked Vince Senior, he respected the man and liked working for him. He tolerated (but didn't particularly like) Vince Junior and helped him out only out of respect for Vince Senior.
6. Bruiser Brody. Oh wait, you said since 1990. Okay...Vader in Japan and WCW before Hulk Hogan killed the monster by not selling any of Vader's offense. Before Hogan sabotaged Vader's career Vader was the monster everybody was afraid of and very few could beat.
7. Without a doubt. Taker is a better wrestler, no question. But Andre was 6 inches taller, nearly 200 pounds larger, and Taker's power offense wouldn't be very effective against The Giant. Andre was too big, too tough, and too strong.
BQ: That was to get The Million Dollar Man over as a despicable low-life rat bastard heel who would BUY a World Title rather than get in the ring and win it himself. As far as I know Andre and Ted Dibiase Senior were friends (they'd worked together in other promotions), and Andre actually liked Hogan, too (or at least liked working with him). Andre did that to help his friends in their storyline. And by that time, Andre's body was breaking down and he could barely walk without assistance. He couldn't be World Champ in the state of health he was in.