Why won't my Mercury Optimax 150 outboard start up. Engine turns over just fine, and there's 2 beeps to the throttle box.

many mercury motors use a rubber mounted prop on the shaft which is a sacrificial idea to prevent gear box damage and prop damage in with under water objects
what you suggests indicates that at certain load situations that rubber has failed and allowing the shaft to turn but is not driving the prop as required
It is driving just enough to give you steerage to get home

go google and type in--- mercury outboard motor manuals --and there are pages of download manuals
if there is not one for your engine then alter the url question to --manual for mercury outboard engine 150hp v6--and see what comes up.

check the cdi

buy a new one from Quicksilver dealer or a breaker !

I have a problem with my 2 stroke 20hp mercury 1989,when I run 10-90% throttle it's works fine but when in 100% its only runs in 90% and doesn't sound normal like it's not burning right.

Dont have the manual in front of me...recollect that there's two types of warnings. The pulsating warning is oil (starts with 30 minutes of oil left) or the fuel filter (or sperator, something like that) may have water in it. Running outboard with cover off, is a little black box that would have a red light lit if that's the case. If oil full & no red light, may be oil injection system...would also check to make sure lines aren't pinched, etc. Mine has been specific to oil the two times its gone off.

The full non-pulsating is engine overheat. Not sure beyond that.

Not much, but hopefully gets you going.