What is the current state of weaponry?

Personal weaponry is primarily blades and firearms. While some personal directed energy weapons have been developed, they are generally bulky and do not have the capability of carrying as much firepower in a small enough package when compared to firearms. Laws vary from place to place as far as what is permitted.

Ship weaponry is different. Different star systems have different laws on what weapons are allowed on civilian ships. Typical weapon systems are missiles for long range and directed energy for short range. Cheaper cannons are also commonly found, particularly on private ships, but on a ship that means ammo storage and loading issues.

Within the Solar system, ship-based weapons and any personal firearms are very strictly prohibited. There is no such thing as a firearms license for a private individual, in any case whatsoever. Punishment for possession on Earth is often life in prison. Supposedly, the UE laws on this matter are supposed to spread to the end of the galaxy, but the UE finds itself unable to enforce the laws. Even still, the UE will sometimes use weapons charges as an excuse to put someone in prison in some cases.

What time of day is it on the ship?

Time isn't kept on a ship like it is on Earth. Different crew members will have different sleep schedules. It may be "morning" for one character, and "evening" for another.

What stardate is it?

The term "stardate" isn't used. Universal interstellar time and date are based on Earth's UTC. The time and date are exactly 200 years in the future from whatever time and date it is.