A The key difference is the position of the handle when the clamp is locked. A horizontal clamp has the handle position horizontally (parallel with the base) when the clamp is locked. A vertical clamp has the handle positioned vertically (perpendicular to the base) when clamped. The intended use you have will decide which you should buy, but be ware that some vertical clamps have a slightly smaller opening range than horizontal ones. Check the specs!

You should prefer vertical clamps if you are making a jig to be used on a table saw, because the horizontal clamps might have their handles interfere with the fence on the saw.
Conversely, if you were going to use the clams on an assembly table, you might prefer the horizontal clamps, because the vertical ones might get in the way by sticking up. (Also, vertical might interfere with a scroll saw, while horizontal might interfere with a drill press or miter saw.) 

A Normally It has a rubber-like hold down foot and a plastic handle. Those would melt at welding temps. Take off the rubber foot and if your weld is far enough away from the clamp, it might do. Best to use a welding clamp.

Although this is a fairly heavy duty clamp it has some rubber parts on it that may begin to melt as the metal parts get hot. This is more suited for use as a woodworkers clamp on a jig for drilling or glue set up.

A You could replace the bolt with a longer one but the rubber end is melted (permanently attached) to the provided bolt. If you got a longer bolt you would want to have something similar to add to the end. If you didn't get the same size you would also need to replace the nuts.

A Only via where you mount it, otherwise no. Mount it higher or lower if needed.

A I installed a Powertec 20306 latch on an upright freezer door that would not seal securely. I adjusted the force needed to open and close the latch to be light enough for my wife to use it with no difficulty.

A To help preserve the oil seal, please make sure to avoid direct sunlight and avoid putting the clamps at a dusty environment. (The preserving temperature should be around 41°F to 77°F, and not over 77°F. We recommend keeping the humidity level at below 70% to avoid the environment being too humid or too dry)