When using a weapon as an improvised weapon you are treating it as an object.:
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.
If the improvised weapon is similar to a real one, then at the DM's discretion you can use its profile instead (thus gaining appropriate 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 DM'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.
As for your examples:
It all depends how you are using it. Keep that in mind.
- Would a thrown Scimitar still be a Finesse or Light weapon? No, that is not how a scimitar is usually used
- Would a Pike still be Heavy or have Reach? Depends how it is being wielded; if held in the middle and used as a quarterstaff then it would lose both
- Would a net still limit you to only making one attack per action? Not if you are just smacking people with it
- Would it still have no effect on a huge or larger creature? It would not be able to restrain anyone
- Would a Lance still have disadvantage if an enemy is nearby and require two hands (unless mounted)? If you are using it as a makeshift pike, then it would be heavy, reach, two-handed