In daily Life, I always trying to focus on single good thought so no
space for bad. When I did something, I tend to analyse it wether it is
good or bad. It is deep most of the time because I am trying to follow
five precepts. It seems like I am doing nothing wrong.
The above is correct, as the Buddha taught Rahula in MN 61.
So I trying to understand deeper clingings (klesha) that are not
visible to outside. Most of the time, I am stuck in a loop
Yes, the above can occur because morality/being good, while being necessary and desirable, can also be a strong source of clinging to 'self'.
In the Dhammapada, it is taught: (i) avoid evil; (ii) do good; (iii) purify the mind. The phrase 'purify the mind' means to purify the mind of attachment/clinging because avoiding evil & doing good can cause attachment/clinging.
I was trying to improve samadhi but it
weaken the sati. Trying to have a single thought feels heavy to mind.
Focus on environment feels calm/less heavy/simple.
The term "sati" or "mindfulness" means "to remember" and "to not forget" to practise the Dhamma Teachings. SN 46.3 says: "a bhikkhu who recollects the Dhamma and thinks it over, on that occasion the enlightenment factor of mindfulness is aroused by the bhikkhu".
Therefore, as shown in your question, sati is required to practise good conduct, as explained in MN 117, as follows:
One is mindful to abandon wrong speech & to enter & remain in right
speech: This is one's right mindfulness. Thus these three qualities —
right view, right effort & right mindfulness — run & circle around
right speech.
One is mindful to abandon wrong action & to enter & remain in right
action: This is one's right mindfulness. Thus these three qualities —
right view, right effort & right mindfulness — run & circle around
right action.
This said, the type or object of sati for the development of morality can be much different to the type or object of sati required for the development of samadhi.
To develop samadhi, the object of sati (remembering) is either the breathing (for beginners) or "letting go" (for mature practitioners), as explained as follows:
There is the case where a monk, having gone to the wilderness, to the shade of a tree, or to an empty building, sits down folding his legs crosswise, holding his body erect, and setting mindfulness to the fore. Always mindful, he breathes in; always mindful he breathes out. MN 118
And what is the faculty of concentration? There is the case where a monk, a disciple of the noble ones, making it his object to let go,
attains concentration, attains singleness of mind. SN 48.10
The mindfulness practise for "letting go" is far more subtle than the mindfulness practise for maintaining good behaviour.
Therefore, as described in your question, as you attempt to develop samadhi, your mindfulness of good behaviour weakens. This probably occurs because your wisdom about what is good & bad behaviour has not yet been fully developed and consolidated.
So How am I improve the situation? I think I have some kind of fear of doing something wrong. Focusing on something good prevent coming
wrong thoughts to mind. I heard these kind of advices from monks. But
this prevent having samdadhi.
Yes, as i explained, this is an ordinary expected obstacle. One of the "fetters" ("obstacles") to Stream-Entry is called "sīlabbata-parāmāsa", which includes crude or clumsy attachment to morality.
I cannot give you any advice about how to improve your situation, apart from encouraging you to be patient. As your sati of good behaviour becomes better and better and more consolidated, I imagine samadhi will naturally develop from this.
Should I have a general idea of good/bad deeds and stop trying to have a single thought always so I can be aware about the environment (have sati)? Have a specific time for a day to reflect about deeds did during the day.
Yes.
When you are around people, you should maintain mindfulness of skillful behaviour & avoiding unskillful behaviour.
When you are alone, you should try to develop mindfulness of one single object, such as the breathing or such as "letting go" of all desires.
Are there any sutta which contrast sati and samadhi?
SN 46.3 says:
"Whenever a bhikkhu who recollects the Dhamma and thinks it over, on that occasion the enlightenment factor of mindfulness is aroused by
the bhikkhu".
"Whenever, bhikkhus, the mind becomes concentrated in a bhikkhu whose body is tranquil and who is happy, on that occasion the
enlightenment factor of concentration is aroused by the bhikkhu."
In summary, sati means to bring & maintain the Teachings in mind. Samadhi means to have a unified mind based on the mind being tranquil & happy.