I don't have many experience in I2c but suspect that I have to use a pull up resistor for SCL and SDA, but when I connect a 10k resistor( I don't have 4.7k right now so I tried with 10K first), the Arduino just return "I2" or "I2C" then stop working and have to be restart
You haven't said what Arduino you have, nor what display you have.
In particular, are they both 5V, or both 3V?
Do you have a secure ground connection between them?
I2C always requires pullups somethwere on both SCL and SDA - the only question is whether these are already built-in to your master and/or slaves.
You will have to consult the documentation for each to find out
I use an Arduino Uno R3
The display I use is not very common, all the document I can find is from Chinese manufacture and all the page about the product wont load
Here are the specs from the seller
because I need a small display and this is the smallest I can find, and I usually don't read the document before I have the product and start working (unless its a important group project), also I think it just like other display and wont have any issue
ran out of solder so I strip the wires and gave them a good twist, my multimeter don't detect any disconnect, may be the main issue is still the lack of pull up resistor, any suggestion so that I can go grab them tomorrow ?
Yes, but that is not guaranteed behavior. The graph is "typical" behavior.
I don't think it serves any useful purpose to advise people that they can directly connect 3.3V and 5V I/O lines, and be confident that their setup will work. There are plenty of posts on this forum reporting destroyed sensors and MCUs as a result.
I always recommend to either use level shifters, or use 3.3V Arduinos with 3.3V devices.