No, the first bullet does not apply to frozen water. It says:
You instantaneously move or otherwise change the flow of the water as you direct, up to 5 feet in any direction. This movement doesn’t have enough force to cause damage.
Frozen water doesn't flow, therefore you can't move it.
Furthermore, assuming you have a weight of ~60kg or 120lb, the necessary force to move you along would be ~600N. That's as much force as a 60kg heavy block of e.g. iron dropped on you from 1 meter above you would have - definitely enough to cause some damage, and hence not permitted.
Yes, but they will only be as good as your DM believes them to be.
Does it qualify as an improvised weapon?
Shape Water allows you to shape water into the form of a simple object, and to freeze this shaped water solid, allowing you to create ice objects.
The rules on improvised weapons have this to say about an object's eligibility to be used as a weapon:
Sometimes characters don’t have their weapons and have to Attack with whatever is at hand. An improvised weapon includes any object you can wield in one or two hands, such as broken glass, a table leg, a frying pan, a wagon wheel, or a dead Goblin.
As long as the ice you've created isn't so big that you cannot wield it in two hands, you can definitely try to use it as an improvised weapon.
What properties will it have?
The rules on improvised weapons have this to say about the weapon's properties:
Often, an improvised weapon is similar to an actual weapon and can be treated as such. For example, a table leg is akin to a club. At the GM’s option, a character proficient with a weapon can use a similar object as if it were that weapon and use his or her proficiency bonus.
An object that bears no resemblance to a weapon deals 1d4 damage (the GM assigns a damage type appropriate to the object). If a character uses a ranged weapon to make a melee Attack, or throws a melee weapon that does not have the thrown property, it also deals 1d4 damage. An improvised thrown weapon has a normal range of 20 feet and a long range of 60 feet.
This makes it clear that just how good your new weapon is depends on your DM's opinion of the object's suitability as a weapon.
You can for sure create an ice sculpture in the shape of a weapon, but the spell makes no mention of allowing you to freeze it in a way that would reinforce it or otherwise give it properties outside than that of regular ice, meaning you cannot make anything more durable than regular ice using this cantrip to freeze water, unless your DM rules that Shape Water has the ability to make super-ice in their campaign.
An ice blade would surely shatter on impact and unless your DM allows you to make it exceedingly sharp, it is not likely to cause any slashing or piercing damage.
You could try to create a heavier weapon to cause bludgeoning but a handle made of regular ice couldn't handle the stress of swinging the weapon. This being said a big enough chunk of ice, such as the head of a maul, has enough mass to inflict real damage on hit.
All of this being considered, the most likely properties of your ice weapon would be to:
- break after very few uses
- deal 1d4 bludgeoning damage
Making it sturdier
You could try to get around the lack of a proper handle and make an okay weapon by freezing the ice around another solid object such as a wooden handle, but in that scenario you would be better off using the more solid object as the weapon itself.
Best Answer
Briefly, no.
If you're going by physics, conservation of energy means that the energy from the vacuum bomb explosion has to come from whatever moves the water, which is the spell. Because the spell doesn't have the force to damage, any vacuum bomb you make also won't have enough energy to deal damage.
D&D is a tabletop RPG, not a physics simulator
D&D is a game that aims to achieve some semblance of balance, and is directed toward being a game. Additionally, the laws of physics don't always mesh with the rules (look at the lack of rules for damage from falling objects).
There are lots of magic effects that could create huge destructive effects from air pressure alone. For example, what about Misty Step? Wouldn't you leave a huge vacuum in the spot that you teleport from, and displace a ton of air where you appear? Could you open a portable hole or bag of holding at low altitude, then open it at high altitude to make a blast of wind? If you cast Gate and make portals between two areas of different altitudes, wouldn't the pressure differential make a powerful, constant wind (see the second to last question)?
These things don't happen in the game because it's a game, and because it's literally magic. If you think too much about the physics of D&D's magic, things break down very quickly. Instead, the world of D&D uses a kind of intuitive fantasy logic.
Of course, this is all up to your DM. If your DM thinks that making a vacuum bomb is a clever, justified use of the spell, then he/she can let it happen. I personally have let a few interesting interpretations of physics slide, just because I thought it would be cool (Fabricating a chunk of radioactive metal into a shape that immediately goes critical, maybe). However, such rulings are DM fiat, and not anything explicitly supported in the written rules.