Especially, at the ages of 50’s.

When I was young, I can stay up to 3:00 am every night and I still feel nothing.

Your sentence starts off by speaking about the past: "When I WAS young ...", so you need to put the next verb (CAN) into the past tense. There are a couple of ways of doing this:

1. "When I was young, I COULD stay up ..."
Here, "could" is a short way of saying "would be able to".
"Could" is used in an "if" sentence, for example: "I could stay up if the occasion demanded it." The staying up was determined by the occasion. Often, the writer does not state the "if" part of the sentence and just leaves it as implied. That's ok.

2. "When I was young, I WAS ABLE to stay up ..."
Here, "was able" provides a more definite and factual statement of ability. It doesn't really need any further emphasis or qualification to get over its meaning.

It is really up to you which one of the above you wish to use. People go for either equally.

Summary:
am able = can (present tense)
example: I am able to stay up/ I can stay up.

was able (past tense statement of fact)
example: I was able to stay up.

would be able = could (past tense conditional)
example: I would be able to stay up (if required)/ I could stay up (if required).

This is not an easy part of English learning, but I hope I have provided you with some of the basics.

But now all I thinking is just go to bed.

"I thinking"
The word "thinking" can be used either as a noun or as part of a verb.
Here, you are using "thinking" as part of a verb. Note, I say PART, so you need to add to it another verb word to make it complete. For example: "But now, all I am thinking ..." Here, AM is the other part of the full verb.

Some other examples:
Present tense: I think, I am thinking
Past tense: I thought, I was thinking.
Future tense: I will think, I will be thinking.

When I was young, I also play snooker for long hours.

"When I was young" is talking about the past.
"I also play" is talking about a present action.
You need to use all past tense verbs here. for example: "When I was young, I also PLAYED snooker ..."
See above for similar explanations about verb tense.

But in between I will have lunch or afternoon tea…

I agree with the previous teacher's comments.
Again, verb tense use is not quite correct here.

Not for straight 6 hours!

I agree withe the previous teacher's comments.

The only good news from this experience.

Needs joining up with the next sentence, as advised by the previous teacher.

My snooker skill is getting steady even under such condition.

As advised by the previous teacher.

Especially, at the ages of 50’s.

You could also phrase it like:

It’s especially hard when you get to be in your fifties.

When I was young, I canould stay up tountil 3:00 am every night and I still feelt nothing.

Instead of “I felt nothing” I might say:

I could stay up til 3 every night and wouldn’t bother me

But nowadays, all I’m thinking is “just go to bed.”

When I was young, I also played snooker for long hours.

But in between I willback then I would take breaks here and there to have lunch or afternoon tea…

You could also say:
But I used to take breaks while playing to etc...

Not for 6 hours straight 6 hours!

Or:
I never played for 6 hours straight!

The only good news from this experience. is that my snooker skills are steadily improving despite the trying conditions.

“The only good news from this experience” isn’t a complete sentence - you’d have to say what the good news is to make it so. So I think combining these two sentences makes sense here.

My snooker skill iss are getting steadybetter even under suchthese condition.s.

This is just another way to say it

I am feeling happysatisfied but this road is too lonely.

To clarify what you mean you by “this road is too lonely” you could say:

I feel satisfied but practicing snooker in this kind of way is a lonely road.