Rear washer motor is working on my vitara but no water comes out.and also the engine goes into limp mode if you stop turn the engine off it runs ok

1 post 2 fails, ok..... ill bite.
no year stated, 1999?in what country, sold all over earth.
and what engine? G16, J20, H25, big differences.
id bet you dont know what limphome is?
but i think you mean CEL glows engine running...
what matters is you didnt scan it,.
get it scanned, guessing the 50 DTC errors is fruitless.
is engine running poorly, misfiring
hard to start,
stalls
shakes,
lost engine power.
ever get a tuneup this decade? spark parts and filters?

the rear washer 99% of time flushing that line fixes it
ask your service, tech, he knows how to flush a line.
it can be clogged at any end to end point, its just a tiny water pump and line, and 1 check valve
or the end nozzle is clogged, the tests are easy.
and not doing this level of basics here.

seem top me the engine, is more pressing need, no?

ask your mech to fix that first then say to him btw.
the rear washer is dead.

Washer jets could be blocked try a drawing pin to clean them. As for limp mode you should have engine management light on if you do use obd scanner for fault code.