Can I conduct independent t-test when data is infested with outliers ? and how to interpret the t-statistics?

1) Maybe, remember that you are assuming a normal distributions, if you don't satisfy those assumptions you are not running a valid test.

2)You are testing whether or not the difference is zero, i.e. no difference=zero in my confidence interval.

3)Bar charts are the easiest to understand because you can see the difference. Box-plots provide more info but are for technical people only.

It's fine to do a t-test on unequal sample size, however, the power wouldn't be as good as equal sample size.

1:) Yes or no. Impossible to say without plotting the outliers. What's more important, can you assume your data be normally distributed? Have you checked the QQ-plot? Have you checked the histogram? Do they look like close to a normal distribution? While the t-test is robust against non-normal data as long as the sample size is sufficient large, your data shouldn't behave too far away from a normal.

When you think about outliers, ask yourself the following questions:

• How many outliers? If you have many, t-test is probably not appropriate.
• Why the outliers? If it's a random error (you're just unlucky), you could include it in the t-test. If it's a systematic error, stop the test, go back and check your data.
• How do you define the outliers?
• Do those outliers look symmetry? If so, you might assume your sample come from a normal population. You can check the skewness of your data.

You have to try to understand those outliers to come with up a decision.

2:) You can just explain like "the probability of the difference in means is (or isn't) significant".

3:) You should draw a box-plot for each group.