Who put up first Christmas Tree?

I can answer one of your questions. The shape of the tree is just the typical shape of the evergreens that are used for Christmas trees. The 'cone' shape is the ideal because it is symmetrical and symmetry is a major characteristic of beauty. Evergreens are the trees used because at this time of year they are the only ones that are not bare, at least in the northern hemisphere.

From Wikipedia again...

The modern custom of erecting a Christmas tree can be traced to 16th century Germany, though neither an inventor nor a single town can be identified as the sole origin for the tradition, which was a popular merging of older traditions mentioned above; in the Cathedral of Strasbourg in 1539, the church record mentions the erection of a Christmas tree. In that period, the guilds started erecting Christmas trees in front of their guildhalls: Ingeborg Weber-Kellermann (Marburg professor of European ethnology) found a Bremen guild chronicle of 1570 which reports how a small fir was decorated with apples, nuts, dates, pretzels and paper flowers, and erected in the guild-house, for the benefit of the guild members' children, who collected the dainties on Christmas day.[8] Another early reference is from Basel, where the tailor apprentices carried around town a tree decorated with apples and cheese in 1597.

We put our tree up two days before Thanksgiving, and then took it down soon after because we thought we were moving out fairly quickly... but ours was up early just the same.