(sorry, got a bit long winded)
The milky stuff from the weep hole is most probably normal - just burnt/unburnt 2 stroke oil, from the exhaust, which is mixed with the cooling water that also goes down the exhaust housing after it has cooled the powerhead.
First I will go over some of the (legacy/common) issues with this model at this age (I own one myself plus a pair of it's "sister's", the 9.9).
They are hard on crank seals when they get older - particularly the upper seal. The seals are cheap (I think about 10 bucks - change quite a few) and easy to change. It's just kinda a little metal (cup) with a rubber membrane that has a spring molded into the rubber. The spring keeps the seal tight against the driveshaft and does a good job of keeping the air/gas/oil, in the crankcase where it belongs until the rubber tears (10-15 years seems to be the typical service life).
At that point, it allows your fuel/oil/air that "should" be going to the cylinders to get blown out into the cowling (upper or lower as the case may be).
A good "tell-tale" for this is either 1) it looks like the powerhead has been sprayed with WD-40 = upper crank is shot or 2) you have an oily/goopey mess in the bottom cowl = lower seal.
In either case the idle "sucks" and they seem "gutless".
Second "issue" I see a lot. Cracked coils. The coils (original) develop very small spider cracks that are tough to see just by looking (because they are usually covered in a film of "gunk".
You can wipe them down well and look for cracks or crazing in the plastic case. If they are suspect they should be replaced but NOT with OEM Merc coils. Sierra coils (18-5186) are not only 1/2 the price of Merc/OEM coils, they are also superior in the amount of power they put out. Merc used to sell a version of them for "portables" called high power or high volt ignition. They will give you a better idle, better cold start and better gas mileage (minimally, but every bit helps especially when they are "cheaper" in the first place).
Third - bad intake gasket. Not behind the carb but on under the transfer cover on the intake on the cylinders (located on the starboard side of the powerhead - right side if you are looking at the prop) up near where the "head" would be if these weren't "headless" models. The cover is a rectangle about 3 or 4" long and maybe an inch wide (with the long side running up/down) - may be partially obscured by the shift linkage.
Anyhow, the little gasket under that cover wears out/blows out which then "transfers" your oil/gas/air NOT into the cylinder but instead into the cowl - obviously results in crappy idle, poor acceleration and all round "crappy" running.
Now, having said all that - AND with any one of them potentially causing your crappy running, I do not think any of them are your issue.
If you are getting water in the cylinder, particularly the lower cylinder I would suspect you have a toasted power head base gasket. Yes, they do go (I have changed/replaced more than a few on these models) and it would cause all the symptoms you note.
On a positive note, while it does require that you remove the powerhead (not very tough on a 15 if you have a manual), the gasket itself is quite cheap (about 6 bucks) and could well solve your issues.
These are outstanding motors - best ignition system ever put on an outboard. Gears are great, carbs are awesome (if you keep them clean) - nothing really negative about the motors. Have never seen a 6/8/9.9/15 Merc 2 stroke that needed a rebuild for any reason other than out and out severe abuse.