do these sentences have the same meaning?

1. Same meaning. Stylistically I prefer the first.

2. The first one is not the greatest sentence ever written; it would mean "an example of someone/something showing integrity". In the second case, the example itself should show integrity. More context is needed in order to ascertain exactly what difference this would make.

3. Neither is correct. You can say "I was in a

GPY1. Same meaning. Stylistically I prefer the first.2. The first one is not the greatest sentence ever written; it would mean "an example of someone/something showing integrity". In the second case, the example itself should show integrity. More context is needed in order to ascertain exactly what difference this would make.3. Neither is correct. You can say "I was in a

jasonkhlimHi GPY.For example: "I was in a blur (on) that day."on that day or that day is modifying / giving more information to the noun, which is blur, right?

No, it's adverbial, describing when you were in a blur.

jasonkhlim4. It is good to do good deeds. It is good doing good deeds.

Just a short note on this one. At the beginning (the subject position) it's more usual to use the -ing form; at the end it's more usual to use the to form.

Doing good deeds is good.
It is good to do good deeds.

For this reason, I can't say

GPY jasonkhlimHi GPY.For example: "I was in a blur (on) that day."on that day or that day is modifying / giving more information to the noun, which is blur, right?No, it's adverbial, describing when you were in a blur.

What about "to play game online"? Is it an adjective?

jasonkhlimWhat about "to play game online"? Is it an adjective?

I assume you are referring to the function of the phrase "to play games online" in the sentence "Is it free to play games online?". No, it does not seem adjectival.