He never was respected like he was today, but he got some fame
William Shakespeare died in 1616.
Shakespeare
It meant what it means now: a long thin candle. Shakespeare liked this word a lot and it is found also in the works of Ben Jonson, Milton and Webster, but not in Marlowe or the King James Bible. It could be a word which Shakespeare propelled into popularity.
Yes.
There are some six surviving specimens of Shakespeare's signature. They are all spelt differently, and none of them say "William Shakespeare." At least one gives his first name as "Guillome", which is a version of William. However, he is now almost universally known as "William Shakespeare."
Shakespeare was born in 1564. He died in 1616. That's fifty-two years.
Pretty much the same as it is now--maybe a little less warm.
By performing in them. Publicity was not Shakespeare's department--he was responsible for writing and performing. Popularity then as now was mostly a matter of word of mouth.
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Latin
Right now his primary characteristic is that he is dead. He is also famous.
Still spinning on its axis, just like it does now.