No. Each piece must be placed in the orientation shown in the tray. Some shapes come in both a horizontal and a vertical version instead.
No. Pieces cannot be rotated or flipped. Place each one exactly as it appears in the tray.
Why this matters
A long horizontal piece needs an unbroken horizontal gap. A vertical gap will not take it, however long it is. Some straight shapes appear in both orientations as separate pieces, so a vertical one can arrive later. Others, such as the L-shaped five-square piece and the T-shape, appear in only one orientation.
Because of this, think about which gaps you are leaving. A gap that only a certain orientation can fill is easy to strand. See the full set of pieces.
Placing without rotating
Drag a piece onto the board to preview it, or tap a piece then a square for its top-left corner. With a keyboard, select a piece, aim with the arrow keys and press Enter or Space. The strategy guide shows how to plan around fixed shapes.