The Photoshop triangle tool location depends on the customization of the application but generally you can find it in the same group as the rectangle, ellipse, polygon, custom etc. If it is not there, it will be in the extras and you can then re-position.
It is basically it is the same as the polygon but you don't have to set the value to 3. You can also modify it by using the interactive controls. It is also live which means you can go back to it at any time if applied as a shape, and change the settings. You can also round the corners of the artwork. The best panel to manipulate the vector is the properties panel (if shape option used) which can be found via the window menu. With the vector selected, you can change the fill color as well as stroke and stroke style as well as add stroke styles / dashes etc
You can set the rounding for the corners as well such as 20px or just have sharp corners using 0px
You can apply it as a shape or pixel etc by the setting in the top left corner. If you go for the shape option then you can use the properties panel to manipulate the settings.
Go for the path option and you can can create repeated paths using add / subtract etc to create a complex design. You can also simply click the selection button to create a quick selection that can be filled with gradients, brush strokes and more
You can go for the pixel mode and apply using the current blending mode and opacity and anti-aliasing. You can apply multiple designs across the image as well as overlap in different colors. You can also go to the edit menu and fade the result and change the blending mode / opacity there.
If you go for the shape, you can also use the properties panel to manipulate the fill color, stroke, rounding etc
You can set the appearance of the fill and stroke etc to black or any color as well as set the stroke to have a dash and other settings such as adding a gradient etc
It is a standard vector layer and as a layer it can have a style added such as bevels and strokes and gradients and shadows. You can create all kinds of effects for it
You can also convert the design into a smart object via the layer menu and smart objects and convert command and with that you can then add smart filters such as blurs and oil paint as well as re-color the design using live adjustments that can be modified at any time. The smart object can then be manipulated in many more ways with filters etc as well as masks
This has slightly changed since the previous versions of the application, the approach is now star ratio and not a star mode ON approach. Go to the settings at the top of the application and set the star ratio to 100% and set the points to 3 and create your design by setting the height and width and angle of the artwork.
Select it and set to shape (top left) and then set the fill to nil and set the stroke to black and set the width to 10px say. Apply the shape. You can, of course, apply it more than once and overlap multiple times
You can use it to create a pattern. Start with a new document with a transparent background and then add your shape to that document. Go to the edit menu and define pattern and save that preset. You can now use the pattern design with features such as the layer menu and new fill layer pattern
View menu and show grid. Select pen in the toolbar and set to shape layer option and set fill to black and set to stroke to no color. Click the pen in top left corner. Click the pen in middle bottom. Click pen t in the top right corner. Click back to the first point. Resize the bounding box and rotate 90 degrees. All kinds of different shapes can be made by using the pen. You can also select the anchor points and move them to create different triangles. You can select an anchor point by using direct selection and shift an anchor point and select another anchor point and shift etc. You can then create many new designs with the direct selection.