I will address your questions one-by-one:

1. Summary statistics are always useful, it's good to try to understand your data rather than rely merely on tests and p-values. Do report them, look at the data, use graphs and think hard about what it all means.

2. What you should do depends on your objectives (decision to go on with the treatment? publication? student paper?) Broadly speaking, the reason to perform statistical inference like confidence intervals is that such data are very noisy. Therefore, you would expect some differences to occur by chance and you want ways to sort out what could be the result of sampling variability, how big the effect of your treatment could be and whether the effect you see is likely to generalize well beyond your study. Without that, you run the risk of over-interpreting the pattern of results in your particular sample.

3. All the techniques you mention are in fact closely related but they are problematic for count data. Also, considering each variable individually can be misleading (especially those that obviously cannot be randomized like age, gender, race…). For example, it's entirely possible to have a large and significant difference between race as revealed by a one-way ANOVA that disappears once you consider, say, pathologic stage (e.g. because some group seeks treatment later). Detecting and interpreting this kind of things is not trivial.

4. See 3

5. See 3

6. This looks like the best approach and as explained by @rbatt, Poisson regression/Generalized linear models would be a good guess but building and understanding such models is a large and complex area. This should give you a good starting point to find books on the topic or ask/read more specific questions on this site but you should not expect to go from wondering if a t-test can be used to compare groups to competently analyze a complex clinical trial in a few hours. If your main objective is getting results ASAP rather than learning, seeking advice from a more experienced researcher, or better yet, a statistician (either by hiring a consultant or checking if your employer already has statisticians on staff) is probably the only reasonable solution.

I will address your questions one-by-one:

1. Summary statistics are always useful, it's good to try to understand your data rather than rely merely on tests and p-values. Do report them, look at the data, use graphs and think hard about what it all means.

2. What you should do depends on your objectives (decision to go on with the treatment? publication? student paper?) Broadly speaking, the main reason to perform statistical inference in clinical trials is that such data are very noisy. Therefore, you would expect some differences to occur by chance and you want ways to sort out what could be the result of sampling variability, how big the effect of your treatment could be and whether the effect you see is likely to generalize well beyond your study. Without that, you run the risk of over-interpreting the pattern of results in your particular sample.

3. All the techniques you mention are in fact closely related but they are problematic for count data. Also, considering each variable individually can be misleading (especially those that obviously cannot be randomized like age, gender, race…). For example, it's entirely possible to have a large and significant difference between race as revealed by a one-way ANOVA that disappears once you consider, say, pathologic stage (e.g. because some group seeks treatment later). Detecting and interpreting this kind of things is not trivial.

4. See 3

5. See 3

6. This looks like the best approach and as explained by @rbatt, Poisson regression/Generalized linear models would be a good guess but building and understanding such models is a large and complex area. Knowing what to look for should give you a good starting point to find books on the topic or ask/read more specific questions on this site but you should not expect to go from wondering if a t-test can be used to compare groups to competently analyze a complex clinical trial in a few hours. If your main objective is getting results ASAP rather than learning, seeking advice from a more experienced researcher, or better yet, a statistician (either by hiring a consultant or checking if your employer already has statisticians on staff) is probably the only reasonable solution.