There is not a singular and direct answer to this question, simply because anyone could put together a skateboard for a specific type of riding and make an argument that it was another type of skateboard. This question inquires about "types" of skateboards. I'll answer assuming you mean types as opposed to brands.
Street skateboards are boards designed and evolved for modern street Skateboarding, which consists of but is not limited to tricks and moves performed on flatground, down stairs or over gaps, on ledges and handrails of all kinds, as well as any kind of pipe, wall, corner, angle, curb, bump, jump that can be skated. These are generally, but are not limited to, boards in the 7.4" to 8.75" width range, generally between 30" and 33" long, with a wheelbase between 14.5 and 16" long. Typical wheels range from 49mm to 57mm in size, although there are no rules and people will ride whatever they are comfortable with. The boards tend to have a concave, but there are probably 50 different "kinds" or subtleties in how manufacturers make concave, and that's a subject too broad for this forum, or at least this question.
Vertical skateboards are very similar, but might tend to be in the wider range, with wider, more stable trucks than are commonly used on street boards, with larger wheels in the 55mm to 61mm range. Concaves tend to be similar to street boards, although a slightly more extreme concave might be considered normal.
MegaRamp boards tend to be wider, with a longer wheelbase to make the board more stable, wider trucks for the same reason, and wheels in the 58mm to 62mm range.
Pool skaters are a very specialized breed, like park skaters. Most people who skate pools don't think of themselves as anything other than a skateboarder, and as such, their skateboard might be used for getting to the liquor store, for a session at the skatepark, and then for hopping the fence to a backyard pool. Thus, their skateboards might be any combination of street board, vert board, whatever.
Freestyle skateboards might be very similar to a street board, but many skaters who consider themselves freestylers ride a more narrow board, in the 6.5" to 7" wide range, with trucks of the same width and wheels in the 55mm to 60mm range. The wheels tend to be more square on the edges for certain rail tricks, ie, "Primo" tricks, named after 1980's freestyle legend Primo Desiderio, who had a big bag of rail tricks in his repertoire. General, because of the narrow width, freestyle boards have little or no concave.
Downhill skateboards are built for speed, and over the years they have come in many custom shapes and sizes, from 30" x 7" slightly flexible boards with much wider trucks and large wheels in the 65mm range, to very stiff 36" or longer boards with a very long wheelbase and almost no nose or tail, designed for stability at high speeds. Concave is less important here but becomes a personal choice, since many true downhill boards are custom made.
Longboards come in many shapes and sizes. There are very long boards which cruise and push at a very comfortable rate but do not turn especially well, to boards in the 40" range which have specialized trucks to compensate for the board's reduced mobility. Wheels, likewise, come in many shapes and sizes, but tend towards the 60mm size and are often wider for a wider stance and better grip. Concave will be found in many longboards but there are so many shapes and style and purposes that there is probably not a consistent concave type for longboards.
There are many types of just slalom boards, because there are tight cone races and wider "giant slalom" races as well as mixed or "staggered" courses. In general, slalom boards tend to be flexible boards, often with a camber from the nose to tail of the board. The trucks used on true slalom boards are often specialized, and may engage a wedge pad to increase the angle of the truck kingpin, which changes the turning radius of the trucks. Sometimes, racers will use a more angled kingpin on the front truck and a flat kingpin on the back truck to produce a steering effect, with the front truck able to be turned very sharply while the back truck is very stable.
What kind of trick? It depends... There are many kinds of tricks such as flip, grind, lip etc. For different tricks, different people thought of them. For ex. Rodney Mullen invented the"flip" tricks.
ollie, nollie, kickflip, heelflip, nollie heelflip, nollie kickflip, shuvit, 360 shuvit, pop shuvit, 360 popshuvit, nollie shuvit, nollie 360 shuvit, nollie popshuvit, nollie 360 popshuvit, impossible,varial, varial kickflip, variel heelflip, 360 flip, nollie 360 flip ollie 180, ollie 360, laser flip, casper
they are pretty much grabs boneless, airwalk, tail grab, rocket, mctwist, 720, one foot grab, ollie back flip, toe flip, crooked, heel flip
Youtube is a great resource for skateboard tricks as so many people film themselves doing them and post these videos there. In the description for many of the videos there is extensive information about how they have performed the tricks.
Regular Beta flip (non fakie) , Merlin Twist , diamond flip (360 hardflip underflip) , Semi Flip , halfcab nosehook impossible indy grab , Carousel , darkslide , ollie imposter and many others
there are more then 100 skateboarding trick.
No
If you are looking for a lightweight boards with spring loaded pop (helps with tricks such as the ollie and all the tricks after it) and durability the best brands to look at are Plan B (highly recommended) and Flip.
You might do a kick-flip and your lace could get caught in the trucks and if the board is flipping fast enough then it could snap.
theres no average tricks for a specific age, i skateboard and im 13 and i can kickflip varial kickflip, big spin, heelflip, pop shove fs bs etc and i have friends that are my age that can nollie double tre flip. so it depends on how much you practice and how naturaly talented you are
Yea,Flips are better then Element
ollie...kickflips