Hi there and thanks for your question.
I am sorry to hear about this issue.
Profuse diarrhoea is a worrying issue and one he does need to see his vet about.
There are many potential causes including parasites, IBD, a chronic infection, a hormonal disorder etc.
The vet will check him over and may run some tests such as a stool analysis to get a clearer idea of what is going on.
From home, I'd offer a bland diet of chicken and rice to help settle the gut.
Alongside water, I'd offer a rehydration solution such as Oralade.
I'd also start a probiotic anti diarrhoea paste (such as Protexin Prokolin) and ensure we are up to date with a broad acting wormer such as Panacur.
These products are all available over the counter from places like pet shops, veterinary receptions or online.
With ongoing diarrhoea we worry about weight loss, dehydration and low blood sugar and as you say he 'looked like death a couple days', he should be seen urgently by his vet.
Until the diarrhoea has resolved, he will likely continue to have accidents.
We should clean this promptly with an enzymatic cleaner to preven re-soiling.
The eye discharge will be unrelated.
Again, this is not a specific sign and we'd wonder about e.g. blocked tear ducts, a chronic viral infection (such as cat flu), oral inflammation etc.
The vet can check his eyes during his consult, which may include a stain to check for ulcers and flushing the eyes to see if the tear ducts are open.
They will also look inside his mouth to check for any oral inflammation or infection.
It may be he needs e.g. a dental cleaning, antibiotics and/or anti inflammatories.
From home, we can bathe the eyes with cotton wool and warm water.
We should also ensure the air is well ventilated and free of any dust or smoke.
Hopefully he is feeling better soon.