how to test 2x2 table with an one empty cell in admission patients?

I am a clinician working for a community based hospital.

A few days ago, my fellow doctor asked me if I could give some advice for her data.

She was working on cross-sectional study in which she investigated the bad effect of high glucose level to the short term outcomes after certain orthopedic procedures.

Among many outcomes as a perioperative complication, just three acute cerebrovascular accident (CVA) was occurred in the study population within admission period.

She did not decide whether it should be included and investigated as a postoperative complication with other more frequent complications because acute cerebral event were too rarely occurred.

Anyway here is the 2x2 table. All the patients had same orthopedic surgery.

_______________________________ no CVA / CVA occured
Patients with Diabetes Mellitus ( DM) 250 / 3
Patients without Diabetes Mellitus (Control) 800 / 0

1) In this table , How to apply Chi-square or Fisher's exact test ?
If she have more patients suffering from CVA (like 50 patients), does a zero cell avoid to violate the assumption of Chi Square Method?

2) If she wanted to adjust other factors such as age and gender, logistic regression is possible ?
Which method would be applied in this case?

It may be not appropriate data for statistical analysis due to the short term period of observation and rarity of event , but I always do wonder what solution could be most appropriate in these rare events analysis.

Thank you very much for any comment or idea !!!
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1) You can use Fisher's exact test. You can't use a chi-squared test because the assumptions are not met. See here.

2) No, you don't have anywhere near enough events to do this

The bottom line is that with rare events you can't be very precise about your results.