Ryobi 2000PSI Electric Pressure washer

SOURCE: pressure washer stalls out when wand nozzle is released

common for not starting unless trigger engaged as you are turning the pump as well as engine creating pressure,as for stalling pump has unloader valve which is probably in need of grease(use good silicone grease)this allows water to ciculate when trigger released.

SOURCE: When I switch my karcher k4.97 washer on it just

you have an internal crack in the out let head of the machine very comon in thease machine and not expencive to fix

SOURCE: When I switch my karcher k4.97 washer on it just

Well, first the easy bit... the pulsation is caused by the leak, because the machine can't hold pressure when the trigger is released.  The difficult bit is: what to do about it?  Unfortunately, there are several different places where the leak can occur and, even with the cover off, it's usually impossible to be sure exactly where the water's coming from.  In the repair shop where I work, we almost always replace every part that might be causing trouble without even trying to identify the exact source.  To do otherwise will rack the labour costs up so high as to render the job uneconomic.  We reckon that if you can't complete the job in 45 minutes it's not worth it.  Sad really, but such are the realities of our economics.
Anyway, unless you are a really competent handy-person, this is probably a job you won't want to tackle for yourself.  So your choice is either to live with it (and do whatever you can to limit the pulsating time - keep it working or switch it off immediately) or take it to a repair shop.  If you are in the UK, Karcher head office can direct you to a repairer, and I guess the same applies in many other countries too.
If you do want to have a go at it yourself, post another message here and I'll give you as much guidance as I can (but there will be a limit to the amount of detail I can provide, as I can't get in to writing a complete service manual!).

SOURCE: I have a K3 78M electric unit . The motor pulsates

This sounds like an internal leak. If you are handy enough here is a schematic. On B@ it could be #25 is sticking or the valve inside #8 is leaking or the water seals #18 need replacing or #1 is leaking

SOURCE: Pulsating when idle

The motor doesn't pulsate when you are spraying and pulsattes when not spraying is normal otherwise the pressure will just keep building and burn out the pump. However, if you are not using the sprayer right away then the unit should be shut off until your ready to start again.
I hope the answer is helpful, please rate if the answer has helped in any way. Good Luck and have a great weekend.