R1197
Okay, here's a rough outline. Hasn't been playtested, but it looks balanced enough...
To determine HP…
Takes an action to appraise an enemy and how injures they look. Make a Medicine check, DC and information given based off of the tables below. You can make the check to determine a creature’s maximum HP or their current HP. You would have to take this action to know the HP of your allies as well, but appraising an ally is only a bonus action.
DC~ CR/Level
10~ 0-5
15~ 6-10
20~ 11-15
25~ 16-20
Impossible~ 21+
Level of success/failure~ Effect
Failure by 6 or more~ False information! Spew out a random number, the more they failed the more confidently you say it and the wronger it is.
Failure by 1-5~ No information given
Success by up to 5~ You know HP to 100s place
Success by 5 to 10~ You know HP to 10s place
Success by 11 or more~ You know the precise HP
Cause of Death…
Make a Medicine check to determine a creature’s cause of death. Handle as you would a Perception or Arcana check.
Healing…
As an action, using a Healer’s Kit or Herbalism Kit, you can make a DC 15 Medicine check to heal an ally 1d4 hit points or to stabilize them if they are dying. You cannot heal the same target again until they suffer more damage (to avoid spam-healing).
Determining weakness…
As an action, you can make a Medicine roll to determine a creature’s weaknesses and resistances. The DC of the check is the same as that of appraising HP (more powerful creatures are less common, and there’s not as much known about them). If you spend an hour or more on research, you have advantage on the check. On a success, you gain a bit of information, as determined by the chart below.
Level of success/failure~ Effect
Failure by 6 or more~ Spew complete misinformation. Fire elementals? Try using your Flame Tongue. They’re weak to heat.
Failure by 5-1~ You get no information.
Success by up to 5~ You can know one resistance, immunity, or vulnerability of the DM’s choice.
Success by 6-10~ You know 1d4+1 resistances, immunities, or vulnerabilities of the DM’s choice.
Success by 11+~ You know all of the creature’s resistances, immunities and vulnerabilities.
If you really wanted to keep uncertainty in level of success, you could try rolling in secret for the player so that they don't know if they botched or got really accurate. You seem like the type of DM who would do that already...